@book{Schulze1998,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Boundary value problems and singular pseudo-differential operators},
  publisher = {Wiley-VCH},
  address   = {Chichester [u.a.]},
  pages     = {XVI, 637 S.},
  year      = {1998},
  language  = {en}
}
@article{Schulze1997,
  author    = {Schulze, Bert-Wolfgang},
  title     = {Boundary value problems and edges pseudo-differential operators},
  year      = {1997},
  language  = {en}
}
@article{HarutjunjanSchulze2005,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Boundary problems with meromorphic symbols in cylindrical domains},
  issn      = {0170-4214},
  year      = {2005},
  abstract  = {We show relative index formulas for boundary value problems in cylindrical domains and Sobolev spaces with different weights at too. The amplitude functions are meromorphic in the axial covariable and take values in the space of boundary value problems on the cross section of the cylinder. Copyright (c) 2005 John Wiley \& Sons, Ltd},
  language  = {en}
}
@book{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Boundary problems with meromorphic symbols in cylindrical domains},
  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     = {19 S.},
  year      = {2004},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2004,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Boundary problems with meromorphic symbols in cylindrical domains},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26735},
  year      = {2004},
  abstract  = {We show relative index formulas for boundary value problems in cylindrical domains and Sobolev spaces with different weigths at ±∞. The amplitude functions are meromorphic in the axial covariable and take values in the space of boundary value problems on the cross section of the cylinder.},
  language  = {en}
}
@article{KhalilSchulze2017,
  author    = {Khalil, Sara and Schulze, Bert-Wolfgang},
  title     = {Boundary problems on a manifold with edge},
  series = {Asian-European Journal of Mathematics},
  volume    = {10},
  journal   = {Asian-European Journal of Mathematics},
  number    = {2},
  publisher = {World Scientific},
  address   = {Singapore},
  issn      = {1793-5571},
  doi       = {10.1142/S1793557117500875},
  pages     = {43},
  year      = {2017},
  abstract  = {We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel's theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.},
  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}
}
@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}
}
@book{KapanadzeSchulze2003,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Asymptotics of potentials 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     = {34 S.},
  year      = {2003},
  language  = {en}
}
@unpublished{KapanadzeSchulze2003,
  author    = {Kapanadze, David and Schulze, Bert-Wolfgang},
  title     = {Asymptotics of potentials in the edge calculus},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26530},
  year      = {2003},
  abstract  = {Boundary value problems on manifolds with conical singularities or edges contain potential operators as well as trace and Green operators which play a similar role as the corresponding operators in (pseudo-differential) boundary value problems on a smooth manifold. There is then a specific asymptotic behaviour of these operators close to the singularities. We characterise potential operators in terms of actions of cone or edge pseudo-differential operators (in the neighbouring space) on densities supported by sbmanifolds which also have conical or edge singularities. As a byproduct we show the continuity of such potentials as continuous perators between cone or edge Sobolev spaces and subspaces with asymptotics.},
  language  = {en}
}
@book{HarutjunjanSchulze2002,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Asymptotics and relative index on a cylinder with conical cross section},
  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     = {45 S.},
  year      = {2002},
  language  = {en}
}
@unpublished{HarutjunjanSchulze2002,
  author    = {Harutjunjan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Asymptotics and relative index on a cylinder with conical cross section},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26446},
  year      = {2002},
  abstract  = {We study pseudodifferential operators on a cylinder IR x B with cross section B that conical singularities. Configurations of that kind are the local model of cornere singularities with base spaces B. Operators A in our calculus are assumed to have symbols α which are meromorphic in the complex covariable with values in the space of all cone operators on B. In case α is dependent of the axial variable t ∈ IR, we show an explicit formula for solutions of the homogeneous equation. Each non-bjectivity 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{FladSchneiderSchulze2007,
  author    = {Flad, H.-J. and Schneider, R. and Schulze, Bert-Wolfgang},
  title     = {Asymptotic Regularity of Solutions of Hartree-Fock Equations with Coulomb Potential},
  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     = {26 S.},
  year      = {2007},
  language  = {en}
}
@unpublished{FladSchneiderSchulze2007,
  author    = {Flad, Heinz-J{\"u}rgen and Schneider, Reinhold and Schulze, Bert-Wolfgang},
  title     = {Asymptotic regularity of solutions of Hartree-Fock equations with coulomb potential},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-30268},
  year      = {2007},
  abstract  = {We study the asymptotic regularity of solutions of Hartree-Fock equations for Coulomb systems. In order to deal with singular Coulomb potentials, Fock operators are discussed within the calculus of pseudo-differential operators on conical manifolds. First, the non-self-consistent-field case is considered which means that the functions that enter into the nonlinear terms are not the eigenfunctions of the Fock operator itself. We introduce asymptotic regularity conditions on the functions that build up the Fock operator which guarantee ellipticity for the local part of the Fock operator on the open stretched cone R+ × S². This proves existence of a parametrix with a corresponding smoothing remainder from which it follows, via a bootstrap argument, that the eigenfunctions of the Fock operator again satisfy asymptotic regularity conditions. Using a fixed-point approach based on Cances and Le Bris analysis of the level-shifting algorithm, we show via another bootstrap argument, that the corresponding self-consistent-field solutions of the Hartree-Fock equation have the same type of asymptotic regularity.},
  language  = {en}
}
@article{FladHarutyunyanSchulze2016,
  author    = {Flad, H. -J. and Harutyunyan, Gohar and Schulze, Bert-Wolfgang},
  title     = {Asymptotic parametrices of elliptic edge operators},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {7},
  journal   = {Journal of pseudo-differential operators and applications},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-016-0159-7},
  pages     = {321 -- 363},
  year      = {2016},
  abstract  = {We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles.},
  language  = {en}
}
@book{NazajkinskijSchulzeSternin2000,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju.},
  title     = {Applications of noncommutative analysis to operator algebras on singular 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     = {54 S.},
  year      = {2000},
  language  = {en}
}
@article{BuchholzSchulze1997,
  author    = {Buchholz, Thilo and Schulze, Bert-Wolfgang},
  title     = {Anisotropic edges pseudo-differential operators withdiscrete asymptotics},
  year      = {1997},
  language  = {en}
}
@book{FedosovSchulzeTarchanov2000,
  author    = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {Analytic index formulas for elliptic corner 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     = {70 S.},
  year      = {2000},
  language  = {en}
}
@article{ChangKhalilSchulze2021,
  author    = {Chang, Der-Chen and Khalil, Sara and Schulze, Bert-Wolfgang},
  title     = {Analysis on regular corner spaces},
  series = {The journal of geometric analysis},
  volume    = {31},
  journal   = {The journal of geometric analysis},
  number    = {9},
  publisher = {Springer},
  address   = {New York},
  issn      = {1050-6926},
  doi       = {10.1007/s12220-021-00614-3},
  pages     = {9199 -- 9240},
  year      = {2021},
  abstract  = {We establish a new approach of treating elliptic boundary value problems (BVPs) on manifolds with boundary and regular corners, up to singularity order 2. Ellipticity and parametrices are obtained in terms of symbols taking values in algebras of BVPs on manifolds of corresponding lower singularity orders. Those refer to Boutet de Monvel's calculus of operators with the transmission property, see Boutet de Monvel (Acta Math 126:11-51, 1971) for the case of smooth boundary. On corner configuration operators act in spaces with multiple weights. We mainly study the case of upper left entries in the respective 2 x 2 operator block-matrices of such a calculus. Green operators in the sense of Boutet de Monvel (Acta Math 126:11-51, 1971) analogously appear in singular cases, and they are complemented by contributions of Mellin type. We formulate a result on ellipticity and the Fredholm property in weighted corner spaces, with parametrices of analogous kind.},
  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}
}
@book{ManicciaSchulze2002,
  author    = {Maniccia, L. and Schulze, Bert-Wolfgang},
  title     = {An algebra of meromorphic corner 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     = {50 S.},
  year      = {2002},
  language  = {en}
}
@unpublished{ManicciaSchulze2002,
  author    = {Maniccia, L. and Schulze, Bert-Wolfgang},
  title     = {An algebra of meromorphic corner symbols},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-26360},
  year      = {2002},
  abstract  = {Operators on manifolds with corners that have base configurations with geometric singularities can be analysed in the frame of a conormal symbolic structure which is in spirit similar to the one for conical singularities of Kondrat'ev's work. Solvability of elliptic equations and asymptotics of solutions are determined by meromorphic conormal symbols. We study the case when the base has edge singularities which is a natural assumption in a number of applications. There are new phenomena, caused by a specific kind of higher degeneracy of the underlying symbols. We introduce an algebra of meromorphic edge operators that depend on complex parameters and investigate meromorphic inverses in the parameter-dependent elliptic case. Among the examples are resolvents of elliptic differential operators on manifolds with edges.},
  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{Schulze1999,
  author    = {Schulze, Bert-Wolfgang},
  title     = {An algebra of boundary value problems not requiring Shapiro-Lopatinskij 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     = {31 S.},
  year      = {1999},
  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}
}
@article{SchroheSchulze1997,
  author    = {Schrohe, Elmar and Schulze, Bert-Wolfgang},
  title     = {A symbol algebra for pseudodifferential boundary value problems on manifolds with edges},
  year      = {1997},
  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}
}
@book{NazajkinskijSchulzeSternin1998,
  author    = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju.},
  title     = {A semiclassical quantization on manifolds with singularities and the Lefschetz formula for elliptic operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 19},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {25 S.},
  year      = {1998},
  language  = {en}
}
@unpublished{FedosovSchulzeTarkhanov1998,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A remark on the index of symmetric operators},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25169},
  year      = {1998},
  abstract  = {We introduce a natural symmetry condition for a pseudodifferential operator on a manifold with cylindrical ends ensuring that the operator admits a doubling across the boundary. For such operators we prove an explicit index formula containing, apart from the Atiyah-Singer integral, a finite number of residues of the logarithmic derivative of the conormal symbol.},
  language  = {en}
}
@book{FedosovSchulzeTarchanov1998,
  author    = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {A remark on the index of symmetric operators},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1998, 04},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {12 S.},
  year      = {1998},
  language  = {en}
}
@article{HedayatMahmoudiSchulze2018,
  author    = {Hedayat Mahmoudi, Mahdi and Schulze, Bert-Wolfgang},
  title     = {A new approach to the second order edge calculus},
  series = {Journal of pseudo-differential operators and applications},
  volume    = {9},
  journal   = {Journal of pseudo-differential operators and applications},
  number    = {2},
  publisher = {Springer},
  address   = {Basel},
  issn      = {1662-9981},
  doi       = {10.1007/s11868-017-0191-2},
  pages     = {265 -- 300},
  year      = {2018},
  abstract  = {We establish essential steps of an iterative approach to operator algebras, ellipticity and Fredholm property on stratified spaces with singularities of second order. We cover, in particular, corner-degenerate differential operators. Our constructions are focused on the case where no additional conditions of trace and potential type are posed, but this case works well and will be considered in a forthcoming paper as a conclusion of the present calculus.},
  language  = {en}
}
@unpublished{NazaikinskiiSchulzeSterninetal.1997,
  author    = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris and Shatalov, Victor},
  title     = {A Lefschetz fixed point theorem for manifolds with conical singularities},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25073},
  year      = {1997},
  abstract  = {We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points.},
  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}
}
@unpublished{FedosovSchulzeTarkhanov1999,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A general index formula on tropic manifolds with conical points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501},
  year      = {1999},
  abstract  = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.},
  language  = {en}
}
@article{FedosovSchulzeTarkhanov2001,
  author    = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A general index formula on toric manifolds with conical point},
  year      = {2001},
  language  = {en}
}
@unpublished{RabinovichSchulzeTarkhanov1997,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich},
  title     = {A calculus of boundary value problems in domains with Non-Lipschitz Singular Points},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-24957},
  year      = {1997},
  abstract  = {The paper is devoted to pseudodifferential boundary value problems in domains with singular points on the boundary. The tangent cone at a singular point is allowed to degenerate. In particular, the boundary may rotate and oscillate in a neighbourhood of such a point. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to singular points.},
  language  = {en}
}
@book{RabinovichSchulzeTarchanov1997,
  author    = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.},
  title     = {A calculus of boundary value problems in domains with Non-Lipschitz singular points},
  series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  volume    = {1997, 09},
  journal   = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik},
  publisher = {Univ.},
  address   = {Potsdam},
  pages     = {54 S.},
  year      = {1997},
  language  = {en}
}