@book{Schulze2003,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Crack theory with singularities at the boundary},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {36 S.},
  year      = {2003},
  language  = {en}
}
@book{Schulze2001,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Operators with symbol hierarchies and iterated asymptotics},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {53 S.},
  year      = {2001},
  language  = {en}
}
@article{Schulze2009,
  author    = {Schulze, Bert-Wolfgang},
  title     = {On a paper of Krupchyk, Tarkhanov, and Tuomela},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2008.07.024},
  year      = {2009},
  abstract  = {We compare the above-mentioned article with the content of a previous publication},
  language  = {en}
}
@unpublished{Schulze2003,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Toeplitz operators, and ellipticity of boundary value problems with global projection conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26510},
  year      = {2003},
  abstract  = {Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators.},
  language  = {en}
}
@unpublished{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Operator algebras with symbol hierarchies on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25647},
  year      = {1999},
  abstract  = {Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.},
  language  = {en}
}
@unpublished{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25596},
  year      = {1999},
  abstract  = {We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.},
  language  = {en}
}
@book{SchulzeDemuthAlbeverioetal.2001,
  author    = {Schulze, Bert-Wolfgang and Demuth, Michael and Albeverio, Sergio and Schrohe, Elmar},
  title     = {Advances in Partial differential equations},
  publisher = {Birkh{\"a}user},
  address   = {Basel},
  year      = {2001},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSternin1999,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir E. and Sternin, Boris},
  title     = {On the homotopy classification of elliptic operators on manifolds with singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25574},
  year      = {1999},
  abstract  = {We study the homotopy classification of elliptic operators on manifolds with singularities and establish necessary and sufficient conditions under which the classification splits into terms corresponding to the principal symbol and the conormal symbol.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSternin1998,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {The index of quantized contact transformations on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25276},
  year      = {1998},
  abstract  = {The quantization of contact transformations of the cosphere bundle over a manifold with conical singularities is described. The index of Fredholm operators given by this quantization is calculated. The answer is given in terms of the Epstein-Melrose contact degree and the conormal symbol of the corresponding operator.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSternin1998,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris},
  title     = {A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25296},
  year      = {1998},
  abstract  = {For general endomorphisms of elliptic complexes on manifolds with conical singularities, the semiclassical asymptotics of the Atiyah-Bott-Lefschetz number is calculated in terms of fixed points of the corresponding canonical transformation of the symplectic space.},
  language  = {en}
}
@unpublished{SchulzeNazaikinskiiSterninetal.1997,
  author    = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir and Sternin, Boris and Shatalov, Victor},
  title     = {Spectral boundary value problems and elliptic equations on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25147},
  year      = {1997},
  abstract  = {For elliptic operators on manifolds with boundary, we define spectral boundary value problems, which generalize the Atiyah-Patodi-Singer problem to the case of nonhomogeneous boundary conditions, operators of arbitrary order, and nonself-adjoint conormal symbols. The Fredholm property is proved and equivalence with certain elliptic equations on manifolds with conical singularities is established.},
  language  = {en}
}
@book{SchulzeNazajkinskijSternin1999,
  author    = {Schulze, Bert-Wolfgang and Nazajkinskij, Vladimir E. and Sternin, Boris Ju.},
  title     = {On the homotopy classification of elliptic operators on manifolds with singularities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {22 S. : graph. Darst.},
  year      = {1999},
  language  = {en}
}
@book{SchulzeQin2005,
  author    = {Schulze, Bert-Wolfgang and Qin, Yuming},
  title     = {Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {53 S.},
  year      = {2005},
  language  = {en}
}
@unpublished{SchulzeQin2005,
  author    = {Schulze, Bert-Wolfgang and Qin, Yuming},
  title     = {Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29892},
  year      = {2005},
  abstract  = {In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.},
  language  = {en}
}
@unpublished{SchulzeSavinSternin1999,
  author    = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris},
  title     = {Elliptic operators in subspaces and the eta invariant},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25496},
  year      = {1999},
  abstract  = {The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.},
  language  = {en}
}
@book{SchulzeSavinSternin1999,
  author    = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris Ju.},
  title     = {The homotopy classification and the index of boundary value problems for general elliptic operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {27 S. : graph. Darst.},
  year      = {1999},
  language  = {en}
}
@article{SchulzeSeiler2006,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Edge operators with conditions of Toeplitz type},
  year      = {2006},
  abstract  = {Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of 2 X 2-block matrix operators with trace and potential operators on the edges. The picture is similar to the pseudodifferential analysis of boundary-value problems. The extra conditions satisfy an analogue of the Shapiro-Lopatinskij condition, provided a topological obstruction for the elliptic edge-degenerate operator in the upper left corner vanishes; this is an analogue of a condition of Atiyah and Bott in boundary-value problems. In general, however, we need global projection data, similarly to global boundary conditions, known for Dirac operators or other geometric operators. The present paper develops a new calculus with global projection data for operators on manifolds with edges. In particular, we show the Fredholm property in a suitable scale of spaces and construct parametrices within the calculus},
  language  = {en}
}
@unpublished{SchulzeSeiler2001,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {The edge algebra structure of boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25955},
  year      = {2001},
  abstract  = {Boundary value problems for pseudodifferential operators (with or without the transmission property) are characterised as a substructure of the edge pseudodifferential calculus with constant discrete asymptotics. The boundary in this case is the edge and the inner normal the model cone of local wedges. Elliptic boundary value problems for non-integer powers of the Laplace symbol belong to the examples as well as problems for the identity in the interior with a prescribed number of trace and potential conditions. Transmission operators are characterised as smoothing Mellin and Green operators with meromorphic symbols.},
  language  = {en}
}
@book{SchulzeSeiler2002,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Pseudodifferential boundary value problems with global projection conditions},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {37 S.},
  year      = {2002},
  language  = {en}
}
@book{SchulzeSeiler2002,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Edge operators with conditions of toeplitz type},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {20 S.},
  year      = {2002},
  language  = {en}
}
@book{SchulzeSeiler2001,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {The edge algebra structure of boundary value problems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {52 S.},
  year      = {2001},
  language  = {en}
}
@article{SchulzeSeiler2004,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Boundary value problems with global projection conditions},
  issn      = {0022-1236},
  year      = {2004},
  abstract  = {Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved},
  language  = {en}
}
@article{SchulzeSeiler2019,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Elliptic complexes on manifolds with boundary},
  series = {The journal of geometric analysis},
  volume    = {29},
  journal   = {The journal of geometric analysis},
  number    = {1},
  publisher = {Springer},
  address   = {New York},
  issn      = {1050-6926},
  doi       = {10.1007/s12220-018-0014-6},
  pages     = {656 -- 706},
  year      = {2019},
  abstract  = {We show that elliptic complexes of (pseudo) differential operators on smooth compact manifolds with boundary can always be complemented to a Fredholm problem by boundary conditions involving global pseudodifferential projections on the boundary (similarly as the spectral boundary conditions of Atiyah, Patodi, and Singer for a single operator). We prove that boundary conditions without projections can be chosen if, and only if, the topological Atiyah-Bott obstruction vanishes. These results make use of a Fredholm theory for complexes of operators in algebras of generalized pseudodifferential operators of Toeplitz type which we also develop in the present paper.},
  language  = {en}
}
@unpublished{SchulzeSeiler2002,
  author    = {Schulze, Bert-Wolfgang and Seiler, J{\"o}rg},
  title     = {Pseudodifferential boundary value problems with global projection conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26233},
  year      = {2002},
  abstract  = {Contents: Introduction 1 Operators with the transmission property 1.1 Operators on a manifold with boundary 1.2 Conditions with pseudodifferential projections 1.3 Projections and Fredholm families 2 Boundary value problems not requiring the transmission property 2.1 Interior operators 2.2 Edge amplitude functions 2.3 Boundary value problems 3 Operators with global projection conditions 3.1 Construction for boundary symbols 3.2 Ellipticity of boundary value problems with projection data 3.3 Operators of order zero},
  language  = {en}
}
@unpublished{SchulzeShlapunovTarkhanov1999,
  author    = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Regularisation of mixed boundary problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25454},
  year      = {1999},
  abstract  = {We show an application of the spectral theorem in constructing approximate solutions of mixed boundary value problems for elliptic equations.},
  language  = {en}
}
@unpublished{SchulzeShlapunovTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {Green integrals on manifolds with cracks},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25777},
  year      = {2000},
  abstract  = {We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D.},
  language  = {en}
}
@book{SchulzeSlapunovTarchanov1999,
  author    = {Schulze, Bert-Wolfgang and Slapunov, Aleksandr A. and Tarchanov, Nikolaj N.},
  title     = {Regularisation of mixed boundary problems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {32 S.},
  year      = {1999},
  language  = {en}
}
@book{SchulzeSlapunovTarchanov2000,
  author    = {Schulze, Bert-Wolfgang and Slapunov, Aleksandr A. and Tarchanov, Nikolaj N.},
  title     = {Green integrals on manifolds with cracks},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {33 S.},
  year      = {2000},
  language  = {en}
}
@article{SchulzeSterninSatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Nonstationary problems for Borel-Fuchs type equations},
  year      = {1997},
  language  = {en}
}
@article{SchulzeSterninSatalov1999,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On the index of elliptic operators on manifolds with conical singularities},
  issn      = {0002-3264},
  year      = {1999},
  language  = {en}
}
@article{SchulzeSterninSatalov1999,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On boundary value problems for elliptic equations},
  issn      = {0002-3264},
  year      = {1999},
  language  = {en}
}
@book{SchulzeSterninSatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On the index of differential operators on manifolds with conical singularities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 10},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {37 S.},
  year      = {1997},
  language  = {en}
}
@book{SchulzeSterninSatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Nonstationary problems for equations of Borel-Fuchs type},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 11},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {34 S.},
  year      = {1997},
  language  = {en}
}
@book{SchulzeSterninSatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On general boundary value problems for elliptic equations},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 35},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {36 S.},
  year      = {1997},
  language  = {en}
}
@article{SchulzeSterninSatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Structure rings of singularities and differential equations},
  year      = {1997},
  language  = {en}
}
@article{SchulzeSterninSatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Operator algebras associated with resurgent transforms and differential equations on manifolds with singularities},
  year      = {1997},
  language  = {en}
}
@article{SchulzeSterninSatalov1994,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Resurgent analysis and differential equations with singularities},
  year      = {1994},
  language  = {en}
}
@article{SchulzeSterninSatalov1995,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Resurgent analysis in the theory of differential equations with singularities},
  year      = {1995},
  language  = {en}
}
@article{SchulzeSterninSatalov1998,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On general boundary value problems for elliptic equations},
  issn      = {0368-8666},
  year      = {1998},
  language  = {en}
}
@article{SchulzeSterninSatalov1998,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On the index of differential operators on manifolds with conical singularities},
  year      = {1998},
  language  = {en}
}
@article{SchulzeSterninSatalov1998,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {An operator algebra on manifolds with cusp type singularities},
  year      = {1998},
  language  = {en}
}
@article{SchulzeSterninSatalov1998,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On general boundary value problems for elliptic equations},
  year      = {1998},
  language  = {en}
}
@article{SchulzeSterninSatalov1998,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {On some global aspects of the theory of partial differential equations on manifolds with singularities},
  year      = {1998},
  language  = {en}
}
@article{SchulzeSterninSatalov1998,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Differential equations on manifolds with singularities in classes of resurgent functions},
  year      = {1998},
  language  = {en}
}
@unpublished{SchulzeSterninSavin1999,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Savin, Anton},
  title     = {The homotopy classification and the index of boundary value problems for general elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25568},
  year      = {1999},
  abstract  = {We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Operator algebras on singular manifolds. I},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25011},
  year      = {1997},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On the index of differential operators on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24965},
  year      = {1997},
  abstract  = {The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Nonstationary problems for equations of Borel-Fuchs type},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24973},
  year      = {1997},
  abstract  = {In the paper, the nonstationary problems for equations of Borel-Fuchs type are investigated. The asymptotic expansion are obtained for different orders of degeneration of operators in question. The approach to nonstationary problems based on the asymptotic theory on abstract algebras is worked out.},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Operator algebras on singular manifolds. IV, V},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25062},
  year      = {1997},
  language  = {en}
}
@unpublished{SchulzeSterninShatalov1997,
  author    = {Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {On general boundary value problems for elliptic equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25138},
  year      = {1997},
  abstract  = {We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved.},
  language  = {en}
}
@book{SchulzeTarchanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Lefschetz theory on manifolds with edges : introduction},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 08},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {20, [4] S,},
  year      = {1997},
  language  = {en}
}
@book{SchulzeTarchanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Asymtotics of solutions to elliptic equations on manifolds with corners},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {62 S.},
  year      = {2000},
  language  = {en}
}
@book{SchulzeTarchanov1999,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Ellipticity and parametrices on manifolds with cuspidal edges},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {53 S.},
  year      = {1999},
  language  = {en}
}
@book{SchulzeTarchanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Pseudodifferential operators on manifolds with corners},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {94 S.},
  year      = {2000},
  language  = {en}
}
@book{SchulzeTarchanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {The Rieman-Roch theorem for manifolds with conical singularities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 18},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {37 S.},
  year      = {1997},
  language  = {en}
}
@article{SchulzeTarchanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {The index of elliptic operators on manifolds with cups},
  year      = {1997},
  language  = {en}
}
@article{SchulzeTarchanov1996,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Coordinate invariance of the wedge Sobolev spaces = Wedge Sobelev spaces},
  year      = {1996},
  language  = {en}
}
@article{SchulzeTarchanov1999,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Elliptic complexes of pseudodifferential operators on manifolds with edges},
  year      = {1999},
  language  = {en}
}
@article{SchulzeTarchanov1999,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Ellipticity and parametrices on manifolds with cuspidal edges},
  year      = {1999},
  language  = {en}
}
@article{SchulzeTarchanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Pseudodifferential calculus on manifolds with singular points},
  issn      = {1311- 0454},
  year      = {1998},
  language  = {en}
}
@article{SchulzeTarchanov1999,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {The Riemann-Roch theorem for manifolds with conical singularities},
  year      = {1999},
  language  = {en}
}
@book{SchulzeTarchanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Elliptic complexes of pseudodifferential operators on manifolds with edges},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 14},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {150 S.},
  year      = {1998},
  language  = {en}
}
@article{SchulzeTarchanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Green pseudodifferential operators on manifolds with edges},
  year      = {1998},
  language  = {en}
}
@book{SchulzeTarchanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Euler solutions of pseudodifferential equations},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 09},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {32 S.},
  year      = {1998},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1999,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Ellipticity and parametrices on manifolds with caspidal edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25411},
  year      = {1999},
  language  = {en}
}
@book{SchulzeTarkhanov2005,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {New algebras of boundary value problems for elliptic pseudodifferential operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {80 S.},
  year      = {2005},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The Riemann-Roch theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25051},
  year      = {1997},
  abstract  = {The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Elliptic complexes of pseudodifferential operators on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25257},
  year      = {1998},
  abstract  = {On a compact closed manifold with edges live pseudodifferential operators which are block matrices of operators with additional edge conditions like boundary conditions in boundary value problems. They include Green, trace and potential operators along the edges, act in a kind of Sobolev spaces and form an algebra with a wealthy symbolic structure. We consider complexes of Fr{\´e}chet spaces whose differentials are given by operators in this algebra. Since the algebra in question is a microlocalization of the Lie algebra of typical vector fields on a manifold with edges, such complexes are of great geometric interest. In particular, the de Rham and Dolbeault complexes on manifolds with edges fit into this framework. To each complex there correspond two sequences of symbols, one of the two controls the interior ellipticity while the other sequence controls the ellipticity at the edges. The elliptic complexes prove to be Fredholm, i.e., have a finite-dimensional cohomology. Using specific tools in the algebra of pseudodifferential operators we develop a Hodge theory for elliptic complexes and outline a few applications thereof.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Pseudodifferential operators on manifolds with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25783},
  year      = {2000},
  abstract  = {We describe an algebra of pseudodifferential operators on a manifold with corners.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2005,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Boundary value problems with Toeplitz conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29837},
  year      = {2005},
  abstract  = {We describe a new algebra of boundary value problems which contains Lopatinskii elliptic as well as Toeplitz type conditions. These latter are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. Every elliptic operator is proved to admit up to a stabilisation elliptic conditions of such a kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. The crucial novelty consists of the new type of weighted Sobolev spaces which serve as domains of pseudodifferential operators and which fit well to the nature of operators.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Euler solutions of pseudodifferential equations},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25211},
  year      = {1998},
  abstract  = {We consider a homogeneous pseudodifferential equation on a cylinder C = IR x X over a smooth compact closed manifold X whose symbol extends to a meromorphic function on the complex plane with values in the algebra of pseudodifferential operators over X. When assuming the symbol to be independent on the variable t element IR, we show an explicit formula for solutions of the equation. Namely, to each non-bijectivity point of the symbol in the complex plane there corresponds a finite-dimensional space of solutions, every solution being the residue of a meromorphic form manufactured from the inverse symbol. In particular, for differential equations we recover Euler's theorem on the exponential solutions. Our setting is model for the analysis on manifolds with conical points since C can be thought of as a 'stretched' manifold with conical points at t = -infinite and t = infinite.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1997,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Lefschetz theory on manifolds with edges : introduction},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24948},
  year      = {1997},
  abstract  = {The aim of this book is to develop the Lefschetz fixed point theory for elliptic complexes of pseudodifferential operators on manifolds with edges. The general Lefschetz theory contains the index theory as a special case, while the case to be studied is much more easier than the index problem. The main topics are: - The calculus of pseudodifferential operators on manifolds with edges, especially symbol structures (inner as well as edge symbols). - The concept of ellipticity, parametrix constructions, elliptic regularity in Sobolev spaces. - Hodge theory for elliptic complexes of pseudodifferential operators on manifolds with edges. - Development of the algebraic constructions for these complexes, such as homotopy, tensor products, duality. - A generalization of the fixed point formula of Atiyah and Bott for the case of simple fixed points. - Development of the fixed point formula also in the case of non-simple fixed points, provided that the complex consists of diferential operarators only. - Investigation of geometric complexes (such as, for instance, the de Rham complex and the Dolbeault complex). Results in this direction are desirable because of both purely mathe matical reasons and applications in natural sciences.},
  language  = {en}
}
@unpublished{SchulzeTarkhanov1998,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A Lefschetz fixed point formula in the relative elliptic theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25159},
  year      = {1998},
  abstract  = {A version of the classical Lefschetz fixed point formula is proved for the cohomology of the cone of a cochain mapping of elliptic complexes. As a particular case we show a Lefschetz formula for the relative de Rham cohomology.},
  language  = {en}
}
@book{SchulzeTarkhanov2003,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Symbol algebra for manifolds with cuspidal singularities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {37 S.},
  year      = {2003},
  language  = {en}
}
@unpublished{SchulzeTarkhanov2000,
  author    = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {Asymptotics of solutions to elliptic equatons on manifolds with corners},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25716},
  year      = {2000},
  abstract  = {We show an explicit link between the nature of a singular point and behaviour of the coefficients of the equation, under which formal asymptotic expansions are still available.},
  language  = {en}
}
@unpublished{SchulzeVolpato2004,
  author    = {Schulze, Bert-Wolfgang and Volpato, A.},
  title     = {Green operators in the edge calculus},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26846},
  year      = {2004},
  abstract  = {Green operators on manifolds with edges are known to be an ingredient of parametrices of elliptic (edge-degenerate) operators. They play a similar role as corresponding operators in boundary value problems. Close to edge singularities the Green operators have a very complex asymptotic behaviour. We give a new characterisation of Green edge symbols in terms of kernels with discrete and continuous asymptotics in the axial variable of local model cones.},
  language  = {en}
}
@book{SchulzeVolpato2004,
  author    = {Schulze, Bert-Wolfgang and Volpato, A.},
  title     = {Green operators in the edge calculus},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {24 S.},
  year      = {2004},
  language  = {en}
}
@unpublished{SchulzeWei2008,
  author    = {Schulze, Bert-Wolfgang and Wei, Y.},
  title     = {Edge-boundary problems with singular trace conditions},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30317},
  year      = {2008},
  abstract  = {The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (σψ; σ∂), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary we have a third symbolic component, namely the edge symbol σ∧, referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions in integral form' there may exist singular trace conditions, investigated in [6] on closed' manifolds with edge. Here we concentrate on the phenomena in combination with boundary conditions and edge problem.},
  language  = {en}
}
@article{SchulzeWei2014,
  author    = {Schulze, Bert-Wolfgang and Wei, Y.},
  title     = {The Mellin-edge quantisation for corner operators},
  series = {Complex analysis and operator theory},
  volume    = {8},
  journal   = {Complex analysis and operator theory},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1661-8254},
  doi       = {10.1007/s11785-013-0289-3},
  pages     = {803 -- 841},
  year      = {2014},
  abstract  = {We establish a quantisation of corner-degenerate symbols, here called Mellin-edge quantisation, on a manifold with second order singularities. The typical ingredients come from the "most singular" stratum of which is a second order edge where the infinite transversal cone has a base that is itself a manifold with smooth edge. The resulting operator-valued amplitude functions on the second order edge are formulated purely in terms of Mellin symbols taking values in the edge algebra over . In this respect our result is formally analogous to a quantisation rule of (Osaka J. Math. 37:221-260, 2000) for the simpler case of edge-degenerate symbols that corresponds to the singularity order 1. However, from the singularity order 2 on there appear new substantial difficulties for the first time, partly caused by the edge singularities of the cone over that tend to infinity.},
  language  = {en}
}
@book{SchulzeWei2008,
  author    = {Schulze, Bert-Wolfgang and Wei, Ya-wei},
  title     = {Edge-boundary problems with singular trace conditions},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {21 S.},
  year      = {2008},
  language  = {en}
}
@article{SchulzeWei2009,
  author    = {Schulze, Bert-Wolfgang and Wei, Ya-wei},
  title     = {Edge-boundary problems with singular trace conditions},
  issn      = {0232-704X},
  doi       = {10.1007/s10455-008-9143-7},
  year      = {2009},
  abstract  = {The ellipticity of boundary value problems on a smooth manifold with boundary relies on a two-component principal symbolic structure (sigma(psi), sigma(partial derivative)), consisting of interior and boundary symbols. In the case of a smooth edge on manifolds with boundary, we have a third symbolic component, namely, the edge symbol sigma(boolean AND), referring to extra conditions on the edge, analogously as boundary conditions. Apart from such conditions 'in integral form' there may exist singular trace conditions, investigated in Kapanadze et al., Internal Equations and Operator Theory, 61, 241-279, 2008 on 'closed' manifolds with edge. Here, we concentrate on the phenomena in combination with boundary conditions and edge problem.},
  language  = {en}
}
@phdthesis{Schwarz2020,
  author    = {Schwarz, Michael},
  title     = {Nodal domains and boundary representation for Dirichlet forms},
  school      = {Universit{\"a}t Potsdam},
  pages     = {164},
  year      = {2020},
  language  = {en}
}
@article{SeeligRabeMalemShinitskietal.2020,
  author    = {Seelig, Stefan A. and Rabe, Maximilian Michael and Malem-Shinitski, Noa and Risse, Sarah and Reich, Sebastian and Engbert, Ralf},
  title     = {Bayesian parameter estimation for the SWIFT model of eye-movement control during reading},
  series = {Journal of mathematical psychology},
  volume    = {95},
  journal   = {Journal of mathematical psychology},
  publisher = {Elsevier},
  address   = {San Diego},
  issn      = {0022-2496},
  doi       = {10.1016/j.jmp.2019.102313},
  pages     = {32},
  year      = {2020},
  abstract  = {Process-oriented theories of cognition must be evaluated against time-ordered observations. Here we present a representative example for data assimilation of the SWIFT model, a dynamical model of the control of fixation positions and fixation durations during natural reading of single sentences. First, we develop and test an approximate likelihood function of the model, which is a combination of a spatial, pseudo-marginal likelihood and a temporal likelihood obtained by probability density approximation Second, we implement a Bayesian approach to parameter inference using an adaptive Markov chain Monte Carlo procedure. Our results indicate that model parameters can be estimated reliably for individual subjects. We conclude that approximative Bayesian inference represents a considerable step forward for computational models of eye-movement control, where modeling of individual data on the basis of process-based dynamic models has not been possible so far.},
  language  = {en}
}
@phdthesis{Seiler1997,
  author    = {Seiler, J{\"o}rg},
  title     = {Pseudodifferential Calculus on Manifolds with Non-Compact Edges},
  address   = {Potsdam},
  pages     = {161 S.},
  year      = {1997},
  language  = {en}
}
@article{Seyedhosseini2022,
  author    = {Seyedhosseini, Mehran},
  title     = {A variant of Roe algebras for spaces with cylindrical ends with applications in relative higher index theory},
  series = {Journal of noncommutative geometry},
  volume    = {16},
  journal   = {Journal of noncommutative geometry},
  number    = {2},
  publisher = {European Mathematical Society},
  address   = {Zurich},
  issn      = {1661-6952},
  doi       = {10.4171/JNCG/457},
  pages     = {595 -- 624},
  year      = {2022},
  abstract  = {In this paper, we define a variant of Roe algebras for spaces with cylindrical ends and use this to study questions regarding existence and classification of metrics of positive scalar curvature on such manifolds which are collared on the cylindrical end. We discuss how our constructions are related to relative higher index theory as developed by Chang, Weinberger, and Yu and use this relationship to define higher rho-invariants for positive scalar curvature metrics on manifolds with boundary. This paves the way for the classification of these metrics. Finally, we use the machinery developed here to give a concise proof of a result of Schick and the author, which relates the relative higher index with indices defined in the presence of positive scalar curvature on the boundary.},
  language  = {en}
}
@article{ShakiPinhasFischer2017,
  author    = {Shaki, Samuel and Pinhas, Michal and Fischer, Martin H.},
  title     = {Heuristics and biases in mental arithmetic},
  series = {Thinking \& Reasoning},
  volume    = {24},
  journal   = {Thinking \& Reasoning},
  number    = {2},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1354-6783},
  doi       = {10.1080/13546783.2017.1348987},
  pages     = {138 -- 156},
  year      = {2017},
  abstract  = {Mental arithmetic is characterised by a tendency to overestimate addition and to underestimate subtraction results: the operational momentum (OM) effect. Here, motivated by contentious explanations of this effect, we developed and tested an arithmetic heuristics and biases model that predicts reverse OM due to cognitive anchoring effects. Participants produced bi-directional lines with lengths corresponding to the results of arithmetic problems. In two experiments, we found regular OM with zero problems (e.g., 3+0, 3-0) but reverse OM with non-zero problems (e.g., 2+1, 4-1). In a third experiment, we tested the prediction of our model. Our results suggest the presence of at least three competing biases in mental arithmetic: a more-or-less heuristic, a sign-space association and an anchoring bias. We conclude that mental arithmetic exhibits shortcuts for decision-making similar to traditional domains of reasoning and problem-solving.},
  language  = {en}
}
@article{SharmaHainzlZoeller2023,
  author    = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert},
  title     = {Seismicity parameters dependence on main shock-induced co-seismic stress},
  series = {Geophysical journal international},
  volume    = {235},
  journal   = {Geophysical journal international},
  number    = {1},
  publisher = {Oxford Univ. Press},
  address   = {Oxford},
  issn      = {0956-540X},
  doi       = {10.1093/gji/ggad201},
  pages     = {509 -- 517},
  year      = {2023},
  abstract  = {The Gutenberg-Richter (GR) and the Omori-Utsu (OU) law describe the earthquakes' energy release and temporal clustering and are thus of great importance for seismic hazard assessment. Motivated by experimental results, which indicate stress-dependent parameters, we consider a combined global data set of 127 main shock-aftershock sequences and perform a systematic study of the relationship between main shock-induced stress changes and associated seismicity patterns. For this purpose, we calculate space-dependent Coulomb Stress (\& UDelta;CFS) and alternative receiver-independent stress metrics in the surrounding of the main shocks. Our results indicate a clear positive correlation between the GR b-value and the induced stress, contrasting expectations from laboratory experiments and suggesting a crucial role of structural heterogeneity and strength variations. Furthermore, we demonstrate that the aftershock productivity increases nonlinearly with stress, while the OU parameters c and p systematically decrease for increasing stress changes. Our partly unexpected findings can have an important impact on future estimations of the aftershock hazard.},
  language  = {en}
}
@article{SharmaHainzlZoelleretal.2020,
  author    = {Sharma, Shubham and Hainzl, Sebastian and Z{\"o}ller, Gert and Holschneider, Matthias},
  title     = {Is Coulomb stress the best choice for aftershock forecasting?},
  series = {Journal of geophysical research : Solid earth},
  volume    = {125},
  journal   = {Journal of geophysical research : Solid earth},
  number    = {9},
  publisher = {American Geophysical Union},
  address   = {Washington},
  issn      = {2169-9313},
  doi       = {10.1029/2020JB019553},
  pages     = {12},
  year      = {2020},
  abstract  = {The Coulomb failure stress (CFS) criterion is the most commonly used method for predicting spatial distributions of aftershocks following large earthquakes. However, large uncertainties are always associated with the calculation of Coulomb stress change. The uncertainties mainly arise due to nonunique slip inversions and unknown receiver faults; especially for the latter, results are highly dependent on the choice of the assumed receiver mechanism. Based on binary tests (aftershocks yes/no), recent studies suggest that alternative stress quantities, a distance-slip probabilistic model as well as deep neural network (DNN) approaches, all are superior to CFS with predefined receiver mechanism. To challenge this conclusion, which might have large implications, we use 289 slip inversions from SRCMOD database to calculate more realistic CFS values for a layered half-space and variable receiver mechanisms. We also analyze the effect of the magnitude cutoff, grid size variation, and aftershock duration to verify the use of receiver operating characteristic (ROC) analysis for the ranking of stress metrics. The observations suggest that introducing a layered half-space does not improve the stress maps and ROC curves. However, results significantly improve for larger aftershocks and shorter time periods but without changing the ranking. We also go beyond binary testing and apply alternative statistics to test the ability to estimate aftershock numbers, which confirm that simple stress metrics perform better than the classic Coulomb failure stress calculations and are also better than the distance-slip probabilistic model.},
  language  = {en}
}
@article{ShcherbakovZhuangZoelleretal.2019,
  author    = {Shcherbakov, Robert and Zhuang, Jiancang and Z{\"o}ller, Gert and Ogata, Yosihiko},
  title     = {Forecasting the magnitude of the largest expected earthquake},
  series = {Nature Communications},
  volume    = {10},
  journal   = {Nature Communications},
  publisher = {Nature Publishing Group},
  address   = {London},
  issn      = {2041-1723},
  doi       = {10.1038/s41467-019-11958-4},
  pages     = {11},
  year      = {2019},
  abstract  = {The majority of earthquakes occur unexpectedly and can trigger subsequent sequences of events that can culminate in more powerful earthquakes. This self-exciting nature of seismicity generates complex clustering of earthquakes in space and time. Therefore, the problem of constraining the magnitude of the largest expected earthquake during a future time interval is of critical importance in mitigating earthquake hazard. We address this problem by developing a methodology to compute the probabilities for such extreme earthquakes to be above certain magnitudes. We combine the Bayesian methods with the extreme value theory and assume that the occurrence of earthquakes can be described by the Epidemic Type Aftershock Sequence process. We analyze in detail the application of this methodology to the 2016 Kumamoto, Japan, earthquake sequence. We are able to estimate retrospectively the probabilities of having large subsequent earthquakes during several stages of the evolution of this sequence.},
  language  = {en}
}
@article{ShebalinNarteauZecharetal.2014,
  author    = {Shebalin, Peter N. and Narteau, Clement and Zechar, Jeremy Douglas and Holschneider, Matthias},
  title     = {Combining earthquake forecasts using differential probability gains},
  series = {Earth, planets and space},
  volume    = {66},
  journal   = {Earth, planets and space},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {1880-5981},
  doi       = {10.1186/1880-5981-66-37},
  pages     = {14},
  year      = {2014},
  abstract  = {We describe an iterative method to combine seismicity forecasts. With this method, we produce the next generation of a starting forecast by incorporating predictive skill from one or more input forecasts. For a single iteration, we use the differential probability gain of an input forecast relative to the starting forecast. At each point in space and time, the rate in the next-generation forecast is the product of the starting rate and the local differential probability gain. The main advantage of this method is that it can produce high forecast rates using all types of numerical forecast models, even those that are not rate-based. Naturally, a limitation of this method is that the input forecast must have some information not already contained in the starting forecast. We illustrate this method using the Every Earthquake a Precursor According to Scale (EEPAS) and Early Aftershocks Statistics (EAST) models, which are currently being evaluated at the US testing center of the Collaboratory for the Study of Earthquake Predictability. During a testing period from July 2009 to December 2011 (with 19 target earthquakes), the combined model we produce has better predictive performance - in terms of Molchan diagrams and likelihood - than the starting model (EEPAS) and the input model (EAST). Many of the target earthquakes occur in regions where the combined model has high forecast rates. Most importantly, the rates in these regions are substantially higher than if we had simply averaged the models.},
  language  = {en}
}
@article{ShebalinNarteauHolschneider2012,
  author    = {Shebalin, Peter and Narteau, Clement and Holschneider, Matthias},
  title     = {From alarm-based to rate-based earthquake forecast models},
  series = {Bulletin of the Seismological Society of America},
  volume    = {102},
  journal   = {Bulletin of the Seismological Society of America},
  number    = {1},
  publisher = {Seismological Society of America},
  address   = {Albany},
  issn      = {0037-1106},
  doi       = {10.1785/0120110126},
  pages     = {64 -- 72},
  year      = {2012},
  abstract  = {We propose a conversion method from alarm-based to rate-based earthquake forecast models. A differential probability gain g(alarm)(ref) is the absolute value of the local slope of the Molchan trajectory that evaluates the performance of the alarm-based model with respect to the chosen reference model. We consider that this differential probability gain is constant over time. Its value at each point of the testing region depends only on the alarm function value. The rate-based model is the product of the event rate of the reference model at this point multiplied by the corresponding differential probability gain. Thus, we increase or decrease the initial rates of the reference model according to the additional amount of information contained in the alarm-based model. Here, we apply this method to the Early Aftershock STatistics (EAST) model, an alarm-based model in which early aftershocks are used to identify space-time regions with a higher level of stress and, consequently, a higher seismogenic potential. The resulting rate-based model shows similar performance to the original alarm-based model for all ranges of earthquake magnitude in both retrospective and prospective tests. This conversion method offers the opportunity to perform all the standard evaluation tests of the earthquake testing centers on alarm-based models. In addition, we infer that it can also be used to consecutively combine independent forecast models and, with small modifications, seismic hazard maps with short- and medium-term forecasts.},
  language  = {en}
}
@article{ShinReichFrank2012,
  author    = {Shin, Seoleun and Reich, Sebastian and Frank, Jason},
  title     = {Hydrostatic Hamiltonian particle-mesh (HPM) methods for atmospheric modelling},
  series = {Quarterly journal of the Royal Meteorological Society},
  volume    = {138},
  journal   = {Quarterly journal of the Royal Meteorological Society},
  number    = {666},
  publisher = {Wiley-Blackwell},
  address   = {Hoboken},
  issn      = {0035-9009},
  doi       = {10.1002/qj.982},
  pages     = {1388 -- 1399},
  year      = {2012},
  abstract  = {We develop a hydrostatic Hamiltonian particle-mesh (HPM) method for efficient long-term numerical integration of the atmosphere. In the HPM method, the hydrostatic approximation is interpreted as a holonomic constraint for the vertical position of particles. This can be viewed as defining a set of vertically buoyant horizontal meshes, with the altitude of each mesh point determined so as to satisfy the hydrostatic balance condition and with particles modelling horizontal advection between the moving meshes. We implement the method in a vertical-slice model and evaluate its performance for the simulation of idealized linear and nonlinear orographic flow in both dry and moist environments. The HPM method is able to capture the basic features of the gravity wave to a degree of accuracy comparable with that reported in the literature. The numerical solution in the moist experiment indicates that the influence of moisture on wave characteristics is represented reasonably well and the reduction of momentum flux is in good agreement with theoretical analysis.},
  language  = {en}
}
@article{ShinSommerReichetal.2010,
  author    = {Shin, Seoleun and Sommer, Matthias and Reich, Sebastian and N{\´e}vir, Peter},
  title     = {Evaluation of three spatial discretization schemes with the Galewsky et al. test},
  issn      = {1530-261X},
  doi       = {10.1002/Asl.279},
  year      = {2010},
  abstract  = {We evaluate the Hamiltonian particle methods (HPM) and the Nambu discretization applied to shallow-water equations on the sphere using the test suggested by Galewsky et al. (2004). Both simulations show excellent conservation of energy and are stable in long-term simulation. We repeat the test also using the ICOSWP scheme to compare with the two conservative spatial discretization schemes. The HPM simulation captures the main features of the reference solution, but wave 5 pattern is dominant in the simulations applied on the ICON grid with relatively low spatial resolutions. Nevertheless, agreement in statistics between the three schemes indicates their qualitatively similar behaviors in the long-term integration.},
  language  = {en}
}
@article{ShinZoellerHolschneideretal.2011,
  author    = {Shin, Seoleun and Z{\"o}ller, Gert and Holschneider, Matthias and Reich, Sebastian},
  title     = {A multigrid solver for modeling complex interseismic stress fields},
  series = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  volume    = {37},
  journal   = {Computers \& geosciences : an international journal devoted to the publication of papers on all aspects of geocomputation and to the distribution of computer programs and test data sets ; an official journal of the International Association for Mathematical Geology},
  number    = {8},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0098-3004},
  doi       = {10.1016/j.cageo.2010.11.011},
  pages     = {1075 -- 1082},
  year      = {2011},
  abstract  = {We develop a multigrid, multiple time stepping scheme to reduce computational efforts for calculating complex stress interactions in a strike-slip 2D planar fault for the simulation of seismicity. The key elements of the multilevel solver are separation of length scale, grid-coarsening, and hierarchy. In this study the complex stress interactions are split into two parts: the first with a small contribution is computed on a coarse level, and the rest for strong interactions is on a fine level. This partition leads to a significant reduction of the number of computations. The reduction of complexity is even enhanced by combining the multigrid with multiple time stepping. Computational efficiency is enhanced by a factor of 10 while retaining a reasonable accuracy, compared to the original full matrix-vortex multiplication. The accuracy of solution and computational efficiency depend on a given cut-off radius that splits multiplications into the two parts. The multigrid scheme is constructed in such a way that it conserves stress in the entire half-space.},
  language  = {en}
}
@unpublished{Shlapunov2000,
  author    = {Shlapunov, Alexander},
  title     = {On Iterations of double layer potentials},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25687},
  year      = {2000},
  abstract  = {We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.},
  language  = {en}
}
@book{Shlapunov1999,
  author    = {Shlapunov, Alexander},
  title     = {Iterations of self-adjoint operators and their applications to elliptic systems},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell},
  publisher = {Univ.},
  address   = {Potsdam},
  issn      = {1437-739X},
  pages     = {23 S.},
  year      = {1999},
  language  = {en}
}
@unpublished{Shlapunov1999,
  author    = {Shlapunov, Alexander},
  title     = {Iterations of self-adjoint operators and their applications to elliptic systems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25401},
  year      = {1999},
  abstract  = {Let Hsub(0), Hsub(1) be Hilbert spaces and L : Hsub(0) -> Hsub(1) be a linear bounded operator with ||L|| ≤ 1. Then L*L is a bounded linear self-adjoint non-negative operator in the Hilbert space Hsub(0) and one can use the Neumann series ∑∞sub(v=0)(I - L*L)v L*f in order to study solvability of the operator equation Lu = f. In particular, applying this method to the ill-posed Cauchy problem for solutions to an elliptic system Pu = 0 of linear PDE's of order p with smooth coefficients we obtain solvability conditions and representation formulae for solutions of the problem in Hardy spaces whenever these solutions exist. For the Cauchy-Riemann system in C the summands of the Neumann series are iterations of the Cauchy type integral. We also obtain similar results 1) for the equation Pu = f in Sobolev spaces, 2) for the Dirichlet problem and 3) for the Neumann problem related to operator P*P if P is a homogeneous first order operator and its coefficients are constant. In these cases the representations involve sums of series whose terms are iterations of integro-differential operators, while the solvability conditions consist of convergence of the series together with trivial necessary conditions.},
  language  = {en}
}
@article{ShlapunovTarchanov2022,
  author    = {Shlapunov, Alexander A. and Tarchanov, Nikolaj Nikolaevič},
  title     = {Inverse image of precompact sets and regular solutions to the Navier-Stokes equations},
  series = {Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki},
  volume    = {32},
  journal   = {Vestnik Udmurtskogo Universiteta. Matematika, mechanika, kompʹjuternye nauki},
  number    = {2},
  publisher = {Udmurtskij gosudarstvennyj universitet},
  address   = {Iževsk},
  issn      = {1994-9197},
  doi       = {10.35634/vm220208},
  pages     = {278 -- 297},
  year      = {2022},
  abstract  = {We consider the initial value problem for the Navier-Stokes equations over R-3 x [0, T] with time T > 0 in the spatially periodic setting. We prove that it induces open injective mappings A(s): B-1(s) -> B-2(s-1) where B-1(s), B-2(s-1) are elements from scales of specially constructed function spaces of Bochner-Sobolev typeparametrized with the smoothness index s is an element of N. Finally, we prove that a map Asis surjective if and only if the inverse image A(s)(- 1) (K) of any pre compact set K from the range of the map Asis bounded in the Bochner space L-s([0, T], L-r(T-3))with the Ladyzhenskaya-Prodi-Serrin numbers s, r.},
  language  = {en}
}
@article{ShlapunovTarchanov2021,
  author    = {Shlapunov, Alexander and Tarchanov, Nikolaj Nikolaevič},
  title     = {An open mapping theorem for the Navier-Stokes type equations associated with the de Rham complex over R-n},
  series = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  volume    = {18},
  journal   = {Siberian electronic mathematical reports = Sibirskie ėlektronnye matematičeskie izvestija},
  number    = {2},
  publisher = {Institut Matematiki Imeni S. L. Soboleva},
  address   = {Novosibirsk},
  issn      = {1813-3304},
  doi       = {10.33048/semi.2021.18.108},
  pages     = {1433 -- 1466},
  year      = {2021},
  abstract  = {We consider an initial problem for the Navier-Stokes type equations associated with the de Rham complex over R-n x[0, T], n >= 3, with a positive time T. We prove that the problem induces an open injective mappings on the scales of specially constructed function spaces of Bochner-Sobolev type. In particular, the corresponding statement on the intersection of these classes gives an open mapping theorem for smooth solutions to the Navier-Stokes equations.},
  language  = {en}
}
@unpublished{ShlapunovTarkhanov2016,
  author    = {Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich},
  title     = {An open mapping theorem for the Navier-Stokes equations},
  volume    = {5},
  number    = {10},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-98687},
  pages     = {80},
  year      = {2016},
  abstract  = {We consider the Navier-Stokes equations in the layer R^n x [0,T] over R^n with finite T > 0. Using the standard fundamental solutions of the Laplace operator and the heat operator, we reduce the Navier-Stokes equations to a nonlinear Fredholm equation of the form (I+K) u = f, where K is a compact continuous operator in anisotropic normed H{\"o}lder spaces weighted at the point at infinity with respect to the space variables. Actually, the weight function is included to provide a finite energy estimate for solutions to the Navier-Stokes equations for all t in [0,T]. On using the particular properties of the de Rham complex we conclude that the Fr{\´e}chet derivative (I+K)' is continuously invertible at each point of the Banach space under consideration and the map I+K is open and injective in the space. In this way the Navier-Stokes equations prove to induce an open one-to-one mapping in the scale of H{\"o}lder spaces.},
  language  = {en}
}