@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{LyuSchulze2016, author = {Lyu, Xiaojing and Schulze, Bert-Wolfgang}, title = {Mellin Operators in the Edge Calculus}, series = {Complex analysis and operator theory}, volume = {10}, journal = {Complex analysis and operator theory}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-015-0511-6}, pages = {965 -- 1000}, year = {2016}, abstract = {A manifold M with smooth edge Y is locally near Y modelled on X-Delta x Omega for a cone X-Delta := ( (R) over bar (+) x X)/({0} x X) where Xis a smooth manifold and Omega subset of R-q an open set corresponding to a chart on Y. Compared with pseudo-differential algebras, based on other quantizations of edge-degenerate symbols, we extend the approach with Mellin representations on the r half-axis up to r = infinity, the conical exit of X-boolean AND = R+ x X (sic) (r, x) at infinity. The alternative description of the edge calculus is useful for pseudo-differential structures on manifolds with higher singularities.}, 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} } @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{MahmoudiSchulzeTepoyan2015, author = {Mahmoudi, Mahdi Hedayat and Schulze, Bert-Wolfgang and Tepoyan, Liparit}, title = {Continuous and variable branching asymptotics}, series = {Journal of pseudo-differential operators and applications}, volume = {6}, journal = {Journal of pseudo-differential operators and applications}, number = {1}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-015-0110-3}, pages = {69 -- 112}, year = {2015}, abstract = {The regularity of solutions to elliptic equations on a manifold with singularities, say, an edge, can be formulated in terms of asymptotics in the distance variable r > 0 to the singularity. In simplest form such asymptotics turn to a meromorphic behaviour under applying the Mellin transform on the half-axis. Poles, multiplicity, and Laurent coefficients form a system of asymptotic data which depend on the specific operator. Moreover, these data may depend on the variable y along the edge. We then have y-dependent families of meromorphic functions with variable poles, jumping multiplicities and a discontinuous dependence of Laurent coefficients on y. We study here basic phenomena connected with such variable branching asymptotics, formulated in terms of variable continuous asymptotics with a y-wise discrete behaviour.}, language = {en} } @article{ChangQianSchulze2015, author = {Chang, Der-Chen and Qian, Tao and Schulze, Bert-Wolfgang}, title = {Corner Boundary Value Problems}, series = {Complex analysis and operator theory}, volume = {9}, journal = {Complex analysis and operator theory}, number = {5}, publisher = {Springer}, address = {Basel}, issn = {1661-8254}, doi = {10.1007/s11785-014-0424-9}, pages = {1157 -- 1210}, year = {2015}, abstract = {Boundary value problems on a manifold with smooth boundary are closely related to the edge calculus where the boundary plays the role of an edge. The problem of expressing parametrices of Shapiro-Lopatinskij elliptic boundary value problems for differential operators gives rise to pseudo-differential operators with the transmission property at the boundary. However, there are interesting pseudo-differential operators without the transmission property, for instance, the Dirichlet-to-Neumann operator. In this case the symbols become edge-degenerate under a suitable quantisation, cf. Chang et al. (J Pseudo-Differ Oper Appl 5(2014):69-155, 2014). If the boundary itself has singularities, e.g., conical points or edges, then the symbols are corner-degenerate. In the present paper we study elements of the corresponding corner pseudo-differential calculus.}, language = {en} } @article{LyuQianSchulze2015, author = {Lyu, Xiaojing and Qian, Tao and Schulze, Bert-Wolfgang}, title = {Order filtrations of the edge algebra}, series = {Journal of pseudo-differential operators and applications}, volume = {6}, journal = {Journal of pseudo-differential operators and applications}, number = {3}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-015-0126-8}, pages = {279 -- 305}, year = {2015}, abstract = {By edge algebra we understand a pseudo-differential calculus on a manifold with edge. The operators have a two-component principal symbolic hierarchy which determines operators up to lower order terms. Those belong to a filtration of the corresponding operator spaces. We give a new characterisation of this structure, based on an alternative representation of edge amplitude functions only containing holomorphic edge-degenerate Mellin symbols.}, language = {en} } @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{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} } @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} } @article{RungrottheeraSchulzeWong2014, author = {Rungrottheera, Wannarut and Schulze, Bert-Wolfgang and Wong, M. W.}, title = {Iterative properties of pseudo-differential operators on edge spaces}, series = {Journal of pseudo-differential operators and applications}, volume = {5}, journal = {Journal of pseudo-differential operators and applications}, number = {4}, publisher = {Springer}, address = {Basel}, issn = {1662-9981}, doi = {10.1007/s11868-014-0100-x}, pages = {455 -- 479}, year = {2014}, abstract = {Pseudo-differential operators with twisted symbolic estimates play a large role in the calculus on manifolds with edge singularities. We study here aspects of the underlying abstract concept and establish a new result on iteration of quantizations.}, language = {en} } @article{FladHarutyunyanSchneideretal.2011, author = {Flad, Heinz-J{\"u}rgen and Harutyunyan, Gohar and Schneider, Reinhold and Schulze, Bert-Wolfgang}, title = {Explicit Green operators for quantum mechanical Hamiltonians}, series = {Manuscripta mathematica}, volume = {135}, journal = {Manuscripta mathematica}, number = {3-4}, publisher = {Springer}, address = {New York}, issn = {0025-2611}, doi = {10.1007/s00229-011-0429-x}, pages = {497 -- 519}, year = {2011}, abstract = {We study a new approach to determine the asymptotic behaviour of quantum many-particle systems near coalescence points of particles which interact via singular Coulomb potentials. This problem is of fundamental interest in electronic structure theory in order to establish accurate and efficient models for numerical simulations. Within our approach, coalescence points of particles are treated as embedded geometric singularities in the configuration space of electrons. Based on a general singular pseudo-differential calculus, we provide a recursive scheme for the calculation of the parametrix and corresponding Green operator of a nonrelativistic Hamiltonian. In our singular calculus, the Green operator encodes all the asymptotic information of the eigenfunctions. Explicit calculations and an asymptotic representation for the Green operator of the hydrogen atom and isoelectronic ions are presented.}, 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} } @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} } @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} } @article{Schulze2001, author = {Schulze, Bert-Wolfgang}, title = {Operator algebras with symbol hierarchies on manifolds with singularities}, year = {2001}, 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} } @book{AlbeverioDemuthSchroheetal.2002, author = {Albeverio, Sergio and Demuth, Michael and Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Parabolicity, volterra calculus, and conical singularities : a volume of advances in partial differential equations}, series = {Operator theory : advances and applications}, volume = {138}, journal = {Operator theory : advances and applications}, publisher = {Birkh{\"a}user Verl.}, address = {Basel}, isbn = {3-7643-6906-x}, pages = {358 S.}, year = {2002}, language = {en} } @book{KapanadzeSchulze2003, author = {Kapanadze, David and Schulze, Bert-Wolfgang}, title = {Crack theory and edge singularities}, series = {Mathematics and its applications}, volume = {561}, journal = {Mathematics and its applications}, publisher = {Kluwer Acad. Publ}, address = {Dordrecht}, isbn = {1-4020-1524-0}, pages = {485 S.}, year = {2003}, language = {en} } @article{SchroheSchulze1994, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Boundary value problems in Boutet de Monvel{\"i}s algebra for manifolds with conical singularities I}, year = {1994}, language = {en} } @article{Schulze1994, author = {Schulze, Bert-Wolfgang}, title = {The variable discrete asymptotics in pseudo-differential boundary value problems}, year = {1994}, language = {en} } @article{Schulze1994, author = {Schulze, Bert-Wolfgang}, title = {Pseudo-differential operators, ellipticity and asymptotics on manifolds with edges}, year = {1994}, 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{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{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} } @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{Schulze1995, author = {Schulze, Bert-Wolfgang}, title = {The variable discrete asymptotics in pseudo-differential boundary value problems II}, year = {1995}, language = {en} } @article{SchroheSchulze1995, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Mellin quantization in the cone calculus for Boutet de Monvel{\"i}s algebra}, year = {1995}, language = {en} } @article{Schulze1995, author = {Schulze, Bert-Wolfgang}, title = {Transmission algebras on singular spaces with components of different dimensions}, year = {1995}, language = {en} } @article{SchroheSchulze1995, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Boundary value problems in Boutet de Monvel's algebra for manifolds with conical singularities 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{FedosovSchulze1996, author = {Fedosov, Boris V. and Schulze, Bert-Wolfgang}, title = {On the index elliptic operators on a cone}, year = {1996}, 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{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} } @article{Schulze1997, author = {Schulze, Bert-Wolfgang}, title = {Boundary value problems and edges pseudo-differential operators}, year = {1997}, 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{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{GilSchulzeSeiler1997, author = {Gil, J. B. and Schulze, Bert-Wolfgang and Seiler, J{\"o}rg}, title = {Holomorphic operator-valued symbols for edgedegenerate pseudo-differential operators}, year = {1997}, language = {en} } @article{BuchholzSchulze1997, author = {Buchholz, Thilo and Schulze, Bert-Wolfgang}, title = {Anisotropic edges pseudo-differential operators withdiscrete asymptotics}, 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{SchulzeTarchanov1997, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {The index of elliptic operators on manifolds with cups}, year = {1997}, 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{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} } @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} } @book{FedosovSchulzeTarchanov1997, author = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {On the index formula for singular surfaces}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 31}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {27 S.}, year = {1997}, 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} } @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} } @book{SchulzeSchrohe1997, author = {Schulze, Bert-Wolfgang and Schrohe, Elmar}, title = {Arbeitsgruppe "Partielle Differentialgleichungen und Komplexe Analysis" (seit 1992)}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1997, 12}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {61 S.}, year = {1997}, language = {de} } @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{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{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} } @article{SchulzeTarchanov1998, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Green pseudodifferential operators on manifolds with edges}, year = {1998}, 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{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{SchroheSchulze1998, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Mellin operators in a pseudodifferential calculus for boundary value problems on manifolds with edges}, year = {1998}, language = {en} } @article{BurenkovSchulzeTarchanov1998, author = {Burenkov, V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Extension operators for sobolev spaces commuting with a given transform}, year = {1998}, language = {en} } @article{FedosovSchulzeTarchanov1998, author = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {On the index of elliptice operators on a wedge}, 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} } @book{Schulze1998, author = {Schulze, Bert-Wolfgang}, title = {Differential equations on singular manifolds : semiclassical theory and operator algebras}, series = {Mathematical topics}, volume = {15}, journal = {Mathematical topics}, publisher = {Wiley-VCH}, address = {Berlin [u.a.]}, pages = {376 S.}, year = {1998}, language = {en} } @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} } @book{PaneahSchulze1998, author = {Paneah, Boris and Schulze, Bert-Wolfgang}, title = {On the existence of smooth solutions of the Dirichlet problem for hyperbolic differential equations}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 05}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {11 S.}, year = {1998}, 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} } @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} } @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} } @book{RabinovichSchulzeTarchanov1998, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Boundary value problems in cuspidal wedges}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 24}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {66 S.}, 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} } @book{SavinSchulzeSternin1998, author = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris Ju.}, title = {On the invariant index formulas for spectral boundary value problems}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 18b}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {23 S.}, year = {1998}, 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} } @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} } @book{NacinovichSchulzeTarchanov1998, author = {Nacinovich, Mauro and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Carleman formulas for the Dolbeault cohomology}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, volume = {1998, 10}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik}, publisher = {Univ.}, address = {Potsdam}, pages = {13 Bl.}, year = {1998}, 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 = {Pseudodifferential calculus on manifolds with singular points}, issn = {1311- 0454}, 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 = {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 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 = {On general boundary value problems for elliptic equations}, issn = {0368-8666}, year = {1998}, language = {en} } @article{FedosovSchulzeTarchanov1999, author = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {On the index formula for singular surfaces}, year = {1999}, 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} } @article{SchulzeTarchanov1999, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {The Riemann-Roch theorem for manifolds with conical singularities}, year = {1999}, language = {en} } @article{SavinSchulzeSternin1999, author = {Savin, Anton and Schulze, Bert-Wolfgang and Sternin, Boris Ju.}, title = {On the invariant index formulas for spectral boundary value problems}, year = {1999}, 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{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Iterated asymptotics on corner manifolds}, year = {1999}, language = {en} } @article{SchroheSchulze1999, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Mellin and Green symbols for boundary value problems 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} } @book{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Operator algebras with symbol hierarchies 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 = {31 S.}, year = {1999}, 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{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{SchroheSchulze1999, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Edge-degenerate boundary value problems on cones}, 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 = {14 S.}, year = {1999}, 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{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{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} } @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{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} } @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{RabinovichSchulzeTarchanov1999, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Boundary value problems in domains 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 = {32 S.}, year = {1999}, 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} } @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} } @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{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} }