@article{RungrottheeraSchulze2014,
  author    = {Rungrottheera, Wannarut and Schulze, Bert-Wolfgang},
  title     = {Weighted spaces on corner manifolds},
  series = {Complex variables and elliptic equations},
  volume    = {59},
  journal   = {Complex variables and elliptic equations},
  number    = {12},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {1747-6933},
  doi       = {10.1080/17476933.2013.876416},
  pages     = {1706 -- 1738},
  year      = {2014},
  abstract  = {We study spaces on manifolds with double weights and iterated discrete and continuous asymptotics, and their relationship with corner pseudo-differential operators.},
  language  = {en}
}
@article{ChangMahmoudiSchulze2018,
  author    = {Chang, Der-Chen and Mahmoudi, Mahdi Hedayat and Schulze, Bert-Wolfgang},
  title     = {Volterra operators in the edge-calculus},
  series = {Analysis and Mathematical Physics},
  volume    = {8},
  journal   = {Analysis and Mathematical Physics},
  number    = {4},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1664-2368},
  doi       = {10.1007/s13324-018-0238-4},
  pages     = {551 -- 570},
  year      = {2018},
  abstract  = {We study the Volterra property of a class of anisotropic pseudo-differential operators on R x B for a manifold B with edge Y and time-variable t. This exposition belongs to a program for studying parabolicity in such a situation. In the present consideration we establish non-smoothing elements in a subalgebra with anisotropic operator-valued symbols of Mellin type with holomorphic symbols in the complex Mellin covariable from the cone theory, where the covariable t of t extends to symbolswith respect to t to the lower complex v half-plane. The resulting space ofVolterra operators enlarges an approach of Buchholz (Parabolische Pseudodifferentialoperatoren mit operatorwertigen Symbolen. Ph. D. thesis, Universitat Potsdam, 1996) by necessary elements to a new operator algebra containing Volterra parametrices under an appropriate condition of anisotropic ellipticity. Our approach avoids some difficulty in choosing Volterra quantizations in the edge case by generalizing specific achievements from the isotropic edge-calculus, obtained by Seiler (Pseudodifferential calculus on manifolds with non-compact edges, Ph. D. thesis, University of Potsdam, 1997), see also Gil et al. (in: Demuth et al (eds) Mathematical research, vol 100. Akademic Verlag, Berlin, pp 113-137, 1997; Osaka J Math 37: 221-260, 2000).},
  language  = {en}
}
@book{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 11},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {57 S.},
  year      = {1998},
  language  = {en}
}
@unpublished{BuchholzSchulze1998,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Volterra operators and parabolicity : anisotropic pseudo-differential operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25231},
  year      = {1998},
  abstract  = {Parabolic equations on manifolds with singularities require a new calculus of anisotropic pseudo-differential operators with operator-valued symbols. The paper develops this theory along the lines of sn abstract wedge calculus with strongly continuous groups of isomorphisms on the involved Banach spaces. The corresponding pseodo-diferential operators are continuous in anisotropic wedge Sobolev spaces, and they form an alegbra. There is then introduced the concept of anisotropic parameter-dependent ellipticity, based on an order reduction variant of the pseudo-differential calculus. The theory is appled to a class of parabolic differential operators, and it is proved the invertibility in Sobolev spaces with exponential weights at infinity in time direction.},
  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}
}
@article{Schulze1995,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Transmission algebras on singular spaces with components of different dimensions},
  year      = {1995},
  language  = {en}
}
@book{Schulze2003,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Toeplitz operators, and ellipticity of 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},
  issn      = {1437-739X},
  pages     = {66 S.},
  year      = {2003},
  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}
}
@book{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The zaremba problem with singular interfaces as a corner boundary value problem},
  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     = {48 S.},
  year      = {2004},
  language  = {en}
}
@article{HarutyunyanSchulze2006,
  author    = {Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem with singular interfaces as a corner boundary value problem},
  series = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis},
  volume    = {25},
  journal   = {Potential analysis : an international journal devoted to the interactions between potential theory, probability theory, geometry and functional analysis},
  publisher = {Springer},
  address   = {Dordrecht},
  issn      = {0926-2601},
  doi       = {10.1007/s11118-006-9020-6},
  pages     = {327 -- 369},
  year      = {2006},
  abstract  = {We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y, i.e., Au = f in int X, T (+/-) u = g(+/-) on int Y+/-, where Y is subdivided into subsets Y+/- with an interface Z and boundary conditions T+/- on Y+/- that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z subset of Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in Bull. Sci. Math. ( to appear). With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem with singular interfaces as a corner boundary value problem},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26855},
  year      = {2004},
  abstract  = {We study mixed boundary value problems for an elliptic operator A on a manifold X with boundary Y , i.e., Au = f in int X, T±u = g± on int Y±, where Y is subdivided into subsets Y± with an interface Z and boundary conditions T± on Y± that are Shapiro-Lopatinskij elliptic up to Z from the respective sides. We assume that Z ⊂ Y is a manifold with conical singularity v. As an example we consider the Zaremba problem, where A is the Laplacian and T- Dirichlet, T+ Neumann conditions. The problem is treated as a corner boundary value problem near v which is the new point and the main difficulty in this paper. Outside v the problem belongs to the edge calculus as is shown in [3]. With a mixed problem we associate Fredholm operators in weighted corner Sobolev spaces with double weights, under suitable edge conditions along Z \ {v} of trace and potential type. We construct parametrices within the calculus and establish the regularity of solutions.},
  language  = {en}
}
@book{DinesHarutjunjanSchulze2003,
  author    = {Dines, Nicoleta and Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem in edge sobolev spaces},
  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     = {38 S.},
  year      = {2003},
  language  = {en}
}
@unpublished{DinesHarutjunjanSchulze2003,
  author    = {Dines, Nicoleta and Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The Zaremba problem in edge Sobolev spaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26615},
  year      = {2003},
  abstract  = {Mixed elliptic boundary value problems are characterised by conditions which have a jump along an interface of codimension 1 on the boundary. We study such problems in weighted edge Sobolev spaces and show the Fredholm property and the existence of parametrices under additional conditions of trace and potential type on the interface. Our methods from the calculus of boundary value problems on a manifold with edges will be illustrated by the Zaremba problem and other mixed problems for the Laplace operator.},
  language  = {en}
}
@article{Schulze1995,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The variable discrete asymptotics in pseudo-differential boundary value problems II},
  year      = {1995},
  language  = {en}
}
@article{Schulze1995,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The variable discrete asymptotics in pseudo-differential boundary value problems II},
  year      = {1995},
  language  = {en}
}
@article{Schulze1994,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The variable discrete asymptotics in pseudo-differential boundary value problems},
  year      = {1994},
  language  = {en}
}
@article{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The trajectory attractor for a nonlinear elliptic system in a cylindrical domain with piecewise smooth 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     = {37 S.},
  year      = {1999},
  language  = {en}
}
@book{Schulze2006,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The structure of operators on manifolds with polyhedral 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     = {131 S.},
  year      = {2006},
  language  = {en}
}
@unpublished{Schulze2006,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The structure of operators on manifolds with polyhedral singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30099},
  year      = {2006},
  abstract  = {We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.},
  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}
}
@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{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{HarutjunjanSchulze2006,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {The relative index for corner singularities},
  issn      = {0378-620X},
  doi       = {10.1007/s00020-005-1367-3},
  year      = {2006},
  abstract  = {We study pseudo-differential operators on a cylinder R x B where B has conical singularities. Configurations of that kind are the local model of corner singularities with cross section B. Operators in our calculus are assumed to have symbols a which are meromorphic in the complex covariable with values in the algebra of all cone operators on B. We show an explicit formula for solutions of the homogeneous equation if a is independent of the axial variable t is an element of R. Each non-bijectivity point of the symbol in the complex plane corresponds to a finite-dimensional space of solutions. Moreover, we give a relative index formula},
  language  = {en}
}
@book{MartinSchulze2005,
  author    = {Martin, Calin-Iulian and Schulze, Bert-Wolfgang},
  title     = {The Quantisation of edge symbols},
  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     = {30 S.},
  year      = {2005},
  language  = {en}
}
@unpublished{MartinSchulze2005,
  author    = {Martin, C.-I. and Schulze, Bert-Wolfgang},
  title     = {The quantisation of edge symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-29959},
  year      = {2005},
  abstract  = {We investigate operators on manifolds with edges from the point of view of the symbolic calculus induced by the singularities. We discuss new aspects of the quantisation of edge-degenerate symbols which lead to continuous operators in weighted edge spaces.},
  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}
}
@unpublished{Schulze2008,
  author    = {Schulze, Bert-Wolfgang},
  title     = {The iterative structure of corner operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30353},
  year      = {2008},
  abstract  = {We give a brief survey on some new developments on elliptic operators on manifolds with polyhedral singularities. The material essentially corresponds to a talk given by the author during the Conference "Elliptic and Hyperbolic Equations on Singular Spaces", October 27 - 31, 2008, at the MSRI, University of Berkeley.},
  language  = {en}
}
@book{NazajkinskijSavinSchulzeetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {The index problem 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     = {27 S.},
  year      = {2004},
  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}
}
@book{NazajkinskijSchulzeSternin1998,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju.},
  title     = {The index of quantized contact transformations on manifolds with conical singularities},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 16},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {31 S.},
  year      = {1998},
  language  = {en}
}
@article{NazajkinskijSterninSchulze1999,
  author    = {Nazajkinskij, Vladimir E. and Sternin, Boris Ju. and Schulze, Bert-Wolfgang},
  title     = {The index of quantized contact transformations on manifolds with conical singularities},
  issn      = {0002-3264},
  year      = {1999},
  language  = {en}
}
@book{FedosovSchulzeTarchanov1998,
  author    = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {The index of higher order operators on singular surfaces},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 03},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {27 S.},
  year      = {1998},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of higher order operators on singular surfaces},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25127},
  year      = {1998},
  abstract  = {The index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points contains the Atiyah-Singer integral as well as two additional terms. One of the two is the 'eta' invariant defined by the conormal symbol, and the other term is explicitly expressed via the principal and subprincipal symbols of the operator at conical points. In the preceding paper we clarified the meaning of the additional terms for first-order differential operators. The aim of this paper is an explicit description of the contribution of a conical point for higher-order differential operators. We show that changing the origin in the complex plane reduces the entire contribution of the conical point to the shifted 'eta' invariant. In turn this latter is expressed in terms of the monodromy matrix for an ordinary differential equation defined by the conormal symbol.},
  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}
}
@unpublished{FedosovSchulzeTarkhanov1997,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {The index of elliptic operators on manifolds with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25096},
  year      = {1997},
  abstract  = {For general elliptic pseudodifferential operators on manifolds with singular points, we prove an algebraic index formula. In this formula the symbolic contributions from the interior and from the singular points are explicitly singled out. For two-dimensional manifolds, the interior contribution is reduced to the Atiyah-Singer integral over the cosphere bundle while two additional terms arise. The first of the two is one half of the 'eta' invariant associated to the conormal symbol of the operator at singular points. The second term is also completely determined by the conormal symbol. The example of the Cauchy-Riemann operator on the complex plane shows that all the three terms may be non-zero.},
  language  = {en}
}
@book{FedosovSchulzeTarchanov1997,
  author    = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {The index of elliptic operators on manifolds with conical points},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 24},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {38 S.},
  year      = {1997},
  language  = {en}
}
@article{FedosovSchulzeTarchanov1999,
  author    = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {The index of elliptic operators on manifolds with conical points},
  year      = {1999},
  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}
}
@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}
}
@inproceedings{RungrottheeraChangSchulze2020,
  author    = {Rungrottheera, Wannarut and Chang, Der-Chen and Schulze, Bert-Wolfgang},
  title     = {The edge calculus of singularity order >3},
  series = {Journal of nonlinear and convex analysis : an international journal},
  volume    = {21},
  booktitle = {Journal of nonlinear and convex analysis : an international journal},
  number    = {2},
  publisher = {Yokohama Publishers},
  address   = {Yokohama},
  issn      = {1345-4773},
  pages     = {387 -- 401},
  year      = {2020},
  abstract  = {We study Mellin pseudo-differential algebras on singular straight cones and manifolds with singularity of order >= 3. Those are necessary to express parametrices of elliptic differential operators with a corresponding cornerdegenerate behavior, and we obtain regularity in weighted spaces.},
  language  = {en}
}
@article{ChangHabalSchulze2014,
  author    = {Chang, Der-Chen and Habal, Nadia and Schulze, Bert-Wolfgang},
  title     = {The edge algebra structure of the Zaremba problem},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {5},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {1},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-013-0088-7},
  pages     = {69 -- 155},
  year      = {2014},
  abstract  = {We study mixed boundary value problems, here mainly of Zaremba type for the Laplacian within an edge algebra of boundary value problems. The edge here is the interface of the jump from the Dirichlet to the Neumann condition. In contrast to earlier descriptions of mixed problems within such an edge calculus, cf. (Harutjunjan and Schulze, Elliptic mixed, transmission and singular crack problems, 2008), we focus on new Mellin edge quantisations of the Dirichlet-to-Neumann operator on the Neumann side of the boundary and employ a pseudo-differential calculus of corresponding boundary value problems without the transmission property at the interface. This allows us to construct parametrices for the original mixed problem in a new and transparent way.},
  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}
}
@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{KrainerSchulze2004,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {The Conormal symbolic structure of corner 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     = {47 S.},
  year      = {2004},
  language  = {en}
}
@unpublished{KrainerSchulze2004,
  author    = {Krainer, Thomas and Schulze, Bert-Wolfgang},
  title     = {The conormal symbolic structure of corner boundary value problems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26662},
  year      = {2004},
  abstract  = {Ellipticity of operators on manifolds with conical singularities or parabolicity on space-time cylinders are known to be linked to parameter-dependent operators (conormal symbols) on a corresponding base manifold. We introduce the conormal symbolic structure for the case of corner manifolds, where the base itself is a manifold with edges and boundary. The specific nature of parameter-dependence requires a systematic approach in terms of meromorphic functions with values in edge-boundary value problems. We develop here a corresponding calculus, and we construct inverses of elliptic elements.},
  language  = {en}
}
@article{NazajkinskijSchulzeSterninetal.1999,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {The Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities},
  year      = {1999},
  language  = {en}
}
@article{NazajkinskijSchulzeSterninetal.1999,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {The Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singularities},
  issn      = {0002-3264},
  year      = {1999},
  language  = {en}
}
@book{CalvoMartinSchulze2004,
  author    = {Calvo, D. and Martin, Calin-Iulian and Schulze, Bert-Wolfgang},
  title     = {Symbolic Structures on Corner Manifolds},
  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     = {18 S.},
  year      = {2004},
  language  = {en}
}
@unpublished{KapanadzeSchulze2001,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Symbolic calculus for boundary value problems on manifolds with edges},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26046},
  year      = {2001},
  abstract  = {Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy of symbols. The symbol structure is responsible or ellipicity and for the nature of parametrices within an algebra of "edge-degenerate" pseudo-differential operators. The edge symbol component of that hierarchy takes values in boundary value problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in this theory, in particular, the contribution with holomorphic operatot-valued Mellin symbols. We establish a calculus in s framework of "twisted homogenity" that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces. We then derive an equivalent representation with a particularly transparent composition behaviour.},
  language  = {en}
}
@book{KapanadzeSchulze2001,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Symbolic calcullus for boundary value problems on manifolds with 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     = {39 S.},
  year      = {2001},
  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}
}
@book{NazajkinskijSchulzeSternin2002,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Surgery and the relative index theorem for families of 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     = {21 S.},
  year      = {2002},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2002,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Surgery and the relative index theorem for families of elliptic operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26300},
  year      = {2002},
  abstract  = {We prove a theorem describing the behaviour of the relative index of families of Fredholm operators under surgery performed on spaces where the operators act. In connection with additional conditions (like symmetry conditions) this theorem results in index formulas for given operator families. By way of an example, we give an application to index theory of families of boundary value problems.},
  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}
}
@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}
}
@article{NazajkinskijSchulzeSterninetal.1998,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Spectral boundary value problems and elliptic equations on singular manifolds},
  year      = {1998},
  language  = {en}
}
@article{NazajkinskijSchulzeSterninetal.1999,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Spectral boundary value problems and elliptic equations on manifolds with singularities},
  issn      = {0002-3264},
  year      = {1999},
  language  = {en}
}
@unpublished{JaianiSchulze2004,
  author    = {Jaiani, George and Schulze, Bert-Wolfgang},
  title     = {Some degenerate elliptic systems and applications to cusped plates},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26866},
  year      = {2004},
  abstract  = {The tension-compression vibration of an elastic cusped plate is studied under all the reasonable boundary conditions at the cusped edge, while at the noncusped edge displacements and at the upper and lower faces of the plate stresses are given.},
  language  = {en}
}
@book{JaianiSchulze2004,
  author    = {Jaiani, George V. and Schulze, Bert-Wolfgang},
  title     = {Some degenerate elliptic systems and applications to cousped plates},
  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      = {2004},
  language  = {en}
}
@article{ChangHedayatMahmoudiSchulze2017,
  author    = {Chang, Der-Chen and Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang},
  title     = {Singular degenerate operators},
  series = {Applicable analysis : an international journal},
  volume    = {96},
  journal   = {Applicable analysis : an international journal},
  number    = {14},
  publisher = {Routledge, Taylor \& Francis Group},
  address   = {Abingdon},
  issn      = {0003-6811},
  doi       = {10.1080/00036811.2017.1336546},
  pages     = {2434 -- 2456},
  year      = {2017},
  abstract  = {We outline some simplified and more general method for constructing parametrices on higher singular spaces. We also outline basic ideas on operators on manifolds with conical or edge singularities.},
  language  = {en}
}
@misc{FladHarutyunyanSchulze2015,
  author    = {Flad, Heinz-J{\"u}rgen and Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Singular analysis and coupled cluster theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-102306},
  pages     = {31530 -- 31541},
  year      = {2015},
  abstract  = {The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to shortrange correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.},
  language  = {en}
}
@article{FladHarutyunyanSchulze2015,
  author    = {Flad, Heinz-J{\"u}rgen and Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Singular analysis and coupled cluster theory},
  series = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  volume    = {17},
  journal   = {Physical chemistry, chemical physics : a journal of European Chemical Societies},
  number    = {47},
  publisher = {Royal Society of Chemistry},
  address   = {Cambridge},
  issn      = {1463-9076},
  doi       = {10.1039/c5cp01183c},
  pages     = {31530 -- 31541},
  year      = {2015},
  abstract  = {The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to short-range correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.},
  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{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}
}
@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}
}
@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}
}
@article{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Reduction of orders in boundary value problems without transmission property},
  issn      = {0025-5645},
  year      = {2004},
  abstract  = {Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We employ specific smooth symbols of arbitrary real orders and with parameters, and we show that the associated operators induce isomorphisms between Sobolev spaces on a given manifold with boundary. Such operators for integer orders have the transmission property and belong to the calculus of Boutet de Monvel [1], cf. also [9]. In general, they fit to the algebra of boundary value problems without the transmission property in the sense of [17] and [24]. Order reducing elements of the present kind are useful for constructing parametrices of mixed elliptic problems. We show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We then investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary. We finally construct order reducing operators on a compact manifold with conical singularities and boundary},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2002,
  author    = {Harutjunjan, G. and Schulze, Bert-Wolfgang},
  title     = {Reduction of orders in boundary value problems without the transmission property},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26220},
  year      = {2002},
  abstract  = {Given an algebra of pseudo-differential operators on a manifold, an elliptic element is said to be a reduction of orders, if it induces isomorphisms of Sobolev spaces with a corresponding shift of smoothness. Reductions of orders on a manifold with boundary refer to boundary value problems. We consider smooth symbols and ellipticity without additional boundary conditions which is the relevant case on a manifold with boundary. Starting from a class of symbols that has been investigated before for integer orders in boundary value problems with the transmission property we study operators of arbitrary real orders that play a similar role for operators without the transmission property. Moreover, we show that order reducing symbols have the Volterra property and are parabolic of anisotropy 1; analogous relations are formulated for arbitrary anisotropies. We finally investigate parameter-dependent operators, apply a kernel cut-off construction with respect to the parameter and show that corresponding holomorphic operator-valued Mellin symbols reduce orders in weighted Sobolev spaces on a cone with boundary.},
  language  = {en}
}
@book{HarutjunjanSchulze2002,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Reduction of Orders in Boundary Value Problems without the Transmission Proberty},
  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      = {2002},
  language  = {en}
}
@article{NazajkinskijSchulzeSterninetal.1999,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.},
  title     = {Quantizational of canonical transformations on manifolds with conical singularities},
  issn      = {0002-3264},
  year      = {1999},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {Quantization of symplectic transformations on manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25084},
  year      = {1997},
  abstract  = {The structure of symplectic (canonical) transformations on manifolds with conical singularities is established. The operators associated with these transformations are defined in the weight spaces and their properties investigated.},
  language  = {en}
}
@book{NazajkinskijSchulzeSternin1999,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju.},
  title     = {Quantization of Lagrangian modules},
  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.},
  year      = {1999},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Part II: Quantization by the method of ordered operators (Noncommutative Analysis) : Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25762},
  year      = {2000},
  abstract  = {Content: 0.1 Preliminary Remarks Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems 1.1 Functions of One Operator (Functional Calculi) 1.2 Functions of Several Operators 1.3 Main Formulas of Operator Calculus 1.4 Main Tools of Noncommutative Analysis 1.5 Composition Laws and Ordered Representations},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 3: Applications of noncommutative analysis to operator algebras on singular manifolds},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25801},
  year      = {2000},
  abstract  = {Content: Chapter 3: Applications of Noncommutative Analysis to Operator Algebras on Singular Manifolds 3.1 Statement of the problem 3.2 Operators on the Model Cone 3.3 Operators on the Model Cusp of Order k 3.4 An Application to the Construction of Regularizers and Proof of the Finiteness Theorem},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin1999,
  author    = {Nazaikinskii, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25582},
  year      = {1999},
  abstract  = {In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 2: Exactly soluble commutation relations (The simplest class of classical mechanics)},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25796},
  year      = {2000},
  abstract  = {Content: Chapter 2: Exactly SolubleCommutation Relations (The Simplest Class of Classical Mechanics) 2.1 Some examples 2.2 Lie commutation relations 2.3 Non-Lie (nonlinear) commutation relations},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin2000,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization methods in differential equations : Chapter 11: Noncommutative analysis and high-frequency asymptotics},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25857},
  year      = {2000},
  abstract  = {Content: Chapter 11: Noncommutative Analysis and High-Frequency Asymptotics 11.1 Statement of the Problem 11.2 Mixed Asymptotics: the General Scheme 11.3 The Asymptotic Solution of Main Problem 11.4 Analysis of the Asymptotic Solution},
  language  = {en}
}
@book{NazajkinskijSchulzeSternin1999,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju.},
  title     = {Quantization and the wave packet transform},
  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     = {63 S.},
  year      = {1999},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSternin1999,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {Quantization and the wave packet transform},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25447},
  year      = {1999},
  language  = {en}
}
@article{NazajkinskijSavinSterninetal.2005,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Sternin, Boris Ju. and Schulze, Bert-Wolfgang},
  title     = {Pseudodifferential operators on manifolds with singularities and localization},
  issn      = {1064-5624},
  year      = {2005},
  language  = {en}
}
@article{NazajkinskijSavinSterninetal.2004,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Sternin, Boris Ju. and Schulze, Bert-Wolfgang},
  title     = {Pseudodifferential operators on manifolds with edges},
  issn      = {1064-5624},
  year      = {2004},
  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}
}
@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{NazajkinskijSavinSchulzeetal.2003,
  author    = {Nazajkinskij, Vladimir E. and Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris},
  title     = {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     = {25 S.},
  year      = {2003},
  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}
}
@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}
}
@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}
}
@book{EgorovSchulze1997,
  author    = {Egorov, Jurij V. and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential operators, singularities, applicatons},
  series = {Operator theory},
  volume    = {93},
  journal   = {Operator theory},
  publisher = {Birkh{\"a}user},
  address   = {Basel},
  isbn      = {3-7643-5484-4},
  pages     = {XII; 349 S.},
  year      = {1997},
  language  = {en}
}
@article{Schulze1994,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential operators, ellipticity and asymptotics on manifolds with edges},
  year      = {1994},
  language  = {en}
}
@article{DorschfeldtSchulze1994,
  author    = {Dorschfeldt, Christoph and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential operators with operator-valued symbols in the Mellin-edge-approach},
  year      = {1994},
  language  = {en}
}
@book{KapanadzeSchulze2000,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential Crack Theory},
  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}
}
@unpublished{KapanadzeSchulze2000,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential crack theory},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25759},
  year      = {2000},
  abstract  = {Crack problems are regarded as elements in a pseudo-differential algbra, where the two sdes int S± of the crack S are treated as interior boundaries and the boundary Y of the crack as an edge singularity. We employ the pseudo-differential calculus of boundary value problems with the transmission property near int S± and the edge pseudo-differential calculus (in a variant with Douglis-Nirenberg orders) to construct parametrices od elliptic crack problems (with extra trace and potential conditions along Y) and to characterise asymptotics of solutions near Y (expressed in the framework of continuous asymptotics). Our operator algebra with boundary and edge symbols contains new weight and order conventions that are necessary also for the more general calculus on manifolds with boundary and edges.},
  language  = {en}
}
@book{Schulze2006,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential calculus on Manifolds with geometric 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     = {60 S.},
  year      = {2006},
  language  = {en}
}
@unpublished{Schulze2006,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential calculus on manifolds with geometric singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30204},
  year      = {2006},
  abstract  = {Differential and pseudo-differential operators on a manifold with (regular) geometric singularities can be studied within a calculus, inspired by the concept of classical pseudo-differential operators on a C1 manifold. In the singular case the operators form an algebra with a principal symbolic hierarchy σ = (σj)0≤j≤k, with k being the order of the singularity and σk operator-valued for k ≥ 1. The symbols determine ellipticity and the nature of parametrices. It is typical in this theory that, similarly as in boundary value problems (which are special edge problems, where the edge is just the boundary), there are trace, potential and Green operators, associated with the various strata of the configuration. The operators, obtained from the symbols by various quantisations, act in weighted distribution spaces with multiple weights. We outline some essential elements of this calculus, give examples and also comment on new challenges and interesting problems of the recent development.},
  language  = {en}
}
@article{DorschfeldtGriemeSchulze1997,
  author    = {Dorschfeldt, Christoph and Grieme, Ulrich and Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential calculus in the Fourieredge approach on non-compact manifolds},
  year      = {1997},
  language  = {en}
}
@book{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential calculus and applications to non-smooth configurations},
  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     = {S. i - ii, 135 S.},
  year      = {1999},
  language  = {en}
}
@book{Schulze1994,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Pseudo-differential boundary value problems, conical singularities, and asymptotics},
  series = {Mathematical topics},
  volume    = {4},
  journal   = {Mathematical topics},
  publisher = {Akad.-Verl.},
  address   = {Berlin},
  isbn      = {3-05-501597-5},
  pages     = {580 S.},
  year      = {1994},
  language  = {en}
}
@article{ChangViahmoudiSchulze2016,
  author    = {Chang, D. -C. and Viahmoudi, M. Hedayat and Schulze, Bert-Wolfgang},
  title     = {PSEUDO-DIFFERENTIAL ANALYSIS WITH TWISTED SYMBOLIC STRUCTURE},
  series = {Journal of nonlinear and convex analysis : an international journal},
  volume    = {17},
  journal   = {Journal of nonlinear and convex analysis : an international journal},
  publisher = {Yokohama Publishers},
  address   = {Yokohama},
  issn      = {1345-4773},
  pages     = {1889 -- 1937},
  year      = {2016},
  abstract  = {This paper is devoted to pseudo-differential operators and new applications. We establish necessary extensions of the standard calculus to specific classes of operator-valued symbols occurring in principal symbolic hierarchies of operators on manifolds with singularities or stratified spaces.},
  language  = {en}
}
@article{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Parametrices of mixed elliptic problems},
  issn      = {0025-584X},
  year      = {2004},
  abstract  = {Mixed elliptic problems for differential operators A in a domain Q with smooth boundary Y are studied in the form Au = f in Omega, T+/-u = g+/- on Y+/-, where Y+/- subset of Y are manifolds with a common boundary Z, such that Y- boolean OR Y+ = Y and Y- boolean AND Y+ = z, with boundary conditions T+/- on Y+/- (with smooth coefficients up to Z from the respective side) satisfying the Shapiro-Lopatinskij condition. We consider such problems in standard Sobolev spaces and characterise natural extra conditions on the interface Z with an analogue of Shapiro-Lopatinskij ellipticity for an associated transmission problem on the boundary; then the extended operator is Fredholm. The transmission operators on the boundary with respect to Z belong to a complete pseudo-differential calculus, a modification of the algebra of boundary value problems without the transmission property. We construct parametrices of elliptic elements in that calculus, and we obtain parametrices of the original mixed problems under additional conditions on the interface. We consider the Zaremba problem and other mixed problems for the Laplace operator, determine the number of extra conditions and calculate the index of associated Fredholm operators. (C) 2004 WILEY-VCH Verlag GmbH \& Co. KGaA, Weinheim},
  language  = {en}
}