Dokument-ID Dokumenttyp Verfasser/Autoren Herausgeber Haupttitel Abstract Auflage Verlagsort Verlag Erscheinungsjahr Seitenzahl Schriftenreihe Titel Schriftenreihe Bandzahl ISBN Quelle der Hochschulschrift Konferenzname Quelle:Titel Quelle:Jahrgang Quelle:Heftnummer Quelle:Erste Seite Quelle:Letzte Seite URN DOI Abteilungen OPUS4-49365 Wissenschaftlicher Artikel Chang, Der-Chen; Schulze, Bert-Wolfgang Ellipticity on spaces with higher singularities We study corner-degenerate pseudo-differential operators of any singularity order and develop ellipticity based on the principal symbolic hierarchy, associated with the stratification of the underlying space. We construct parametrices within the calculus and discuss the aspect of additional trace and potential conditions along lower-dimensional strata. Beijing Science China Press 2017 24 Science China Mathematics 60 11 2053 2076 10.1007/s11425-016-0519-9 Institut für Mathematik OPUS4-51219 Wissenschaftlicher Artikel Chang, Der-Chen; Mahmoudi, Mahdi Hedayat; Schulze, Bert-Wolfgang Volterra operators in the edge-calculus 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). Basel Springer 2018 20 Analysis and Mathematical Physics 8 4 551 570 10.1007/s13324-018-0238-4 Institut für Mathematik OPUS4-48217 Wissenschaftlicher Artikel Khalil, Sara; Schulze, Bert-Wolfgang Calculus on a Manifold with Edge and Boundary We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel's algebra (Acta Math 126:11-51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al. Basel Springer 2019 44 Complex analysis and operator theory 13 6 2627 2670 10.1007/s11785-018-0800-y Institut für Mathematik OPUS4-52138 Wissenschaftlicher Artikel Flad, Heinz-Jürgen; Flad-Harutyunyan, Gohar; Schulze, Bert-Wolfgang Ellipticity of the quantum mechanical Hamiltonians In paper (Flad and Harutyunyan in Discrete Contin Dyn Syst 420-429, 2011) is shown that the Hamiltonian of the helium atom in the Born-Oppenheimer approximation, in the case if two particles coincide, is an edge-degenerate operator, which is elliptic in the corresponding edge calculus. The aim of this paper is an analogous investigation in the case if all three particles coincide. More precisely, we show that the Hamiltonian in the mentioned case is a corner-degenerate operator, which is elliptic as an operator in the corner analysis. Basel Springer 2018 17 Journal of pseudo-differential operators and applications 9 3 451 467 10.1007/s11868-017-0201-4 Institut für Mathematik OPUS4-10595 Buch (Monographie) Abed, Jamil; Schulze, Bert-Wolfgang Operators with Corner-degenerate Symbols Potsdam Univ. 2008 47 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-10621 Buch (Monographie) Schulze, Bert-Wolfgang; Wei, Ya-wei Edge-boundary problems with singular trace conditions Potsdam Univ. 2008 21 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-10622 Buch (Monographie) Schulze, Bert-Wolfgang On a paper of Krupchyk, Tarkhanov and Tuomela Potsdam Univ. 2008 12 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-11006 Buch (Monographie) Flad, H.-J.; Schneider, R.; Schulze, Bert-Wolfgang Asymptotic Regularity of Solutions of Hartree-Fock Equations with Coulomb Potential Potsdam Univ. 2007 26 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-11600 Buch (Monographie) Kapanadze, David; Schulze, Bert-Wolfgang; Seiler, Jörg Operators with singular trace conditions on a manifold with edges Potsdam Univ. 2006 33 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-11725 Buch (Monographie) Schulze, Bert-Wolfgang The structure of operators on manifolds with polyhedral singularities Potsdam Univ. 2006 131 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-11912 Buch (Monographie) Schulze, Bert-Wolfgang Elliptic differential operators on Manifolds with Edges Potsdam Univ. 2006 14 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-10230 misc Flad, Heinz-Jürgen; Harutyunyan, Gohar; Schulze, Bert-Wolfgang Singular analysis and coupled cluster theory 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. 2015 12 31530 31541 urn:nbn:de:kobv:517-opus4-102306 Institut für Mathematik OPUS4-12289 Wissenschaftlicher Artikel Harutjunjan, Gohar; Schulze, Bert-Wolfgang The relative index for corner singularities 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 2006 10.1007/s00020-005-1367-3 Institut für Mathematik OPUS4-12277 Wissenschaftlicher Artikel Schulze, Bert-Wolfgang; Seiler, Jörg Edge operators with conditions of Toeplitz type Ellipticity of operators on a manifold with edges can be treated in the framework of a calculus of 2 X 2-block matrix operators with trace and potential operators on the edges. The picture is similar to the pseudodifferential analysis of boundary-value problems. The extra conditions satisfy an analogue of the Shapiro-Lopatinskij condition, provided a topological obstruction for the elliptic edge-degenerate operator in the upper left corner vanishes; this is an analogue of a condition of Atiyah and Bott in boundary-value problems. In general, however, we need global projection data, similarly to global boundary conditions, known for Dirac operators or other geometric operators. The present paper develops a new calculus with global projection data for operators on manifolds with edges. In particular, we show the Fredholm property in a suitable scale of spaces and construct parametrices within the calculus 2006 Institut für Mathematik OPUS4-12800 Buch (Monographie) Harutjunjan, Gohar; Schulze, Bert-Wolfgang Conormal symbols of mixed elliptic problems with singular interfaces Potsdam Univ. 2005 18 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-12991 Buch (Monographie) Schulze, Bert-Wolfgang; Qin, Yuming Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity Potsdam Univ. 2005 53 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-13670 Wissenschaftlicher Artikel Harutjunjan, Gohar; Schulze, Bert-Wolfgang Boundary problems with meromorphic symbols in cylindrical domains 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 2005 Institut für Mathematik OPUS4-13694 Wissenschaftlicher Artikel Kapanadze, David; Schulze, Bert-Wolfgang Boundary-contact problems for domains with conical singularities We study boundary-contact problems for elliptic equations (and systems) with interfaces that have conical singularities. Such problems represent continuous operators between weighted Sobolev spaces and subspaces with asymptotics. Ellipticity is formulated in terms of extra transmission conditions along the interfaces with a control of the conormal symbolic structure near conical singularities. We show regularity and asymptotics of solutions in weighted spaces, and we construct parametrices. The result will be illustrated by a number of explicit examples. (c) 2004 Elsevier Inc. All rights reserved 2005 Institut für Mathematik OPUS4-13649 Wissenschaftlicher Artikel Nazajkinskij, Vladimir E.; Savin, Anton; Sternin, Boris Ju.; Schulze, Bert-Wolfgang Pseudodifferential operators on manifolds with singularities and localization 2005 Institut für Mathematik OPUS4-14016 Buch (Monographie) Liu, Xiaochun; Schulze, Bert-Wolfgang Ellipticity on Manifolds with edges and boundary Potsdam Univ. 2004 35 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-14005 Buch (Monographie) Krainer, Thomas; Schulze, Bert-Wolfgang The Conormal symbolic structure of corner boundary value problems Potsdam Univ. 2004 47 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-14012 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris The index problem on manifolds with singularities Potsdam Univ. 2004 27 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-14082 Buch (Monographie) Kapanadze, David; Schulze, Bert-Wolfgang Boundary-contact Problems for Domains with Conical Singularities Potsdam Univ. 2004 37 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-14235 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Elliptic theory on manifolds with edges Potsdam Univ. 2004 48 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Informatik und Computational Science OPUS4-14236 Buch (Monographie) Liu, Xiaochun; Schulze, Bert-Wolfgang Boundary value problems in edge representation Potsdam Univ. 2004 43 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Informatik und Computational Science OPUS4-14237 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris On the homotopy classification of elliptic operators on manifolds with edges Potsdam Univ. 2004 26 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Informatik und Computational Science OPUS4-14238 Buch (Monographie) Egorov, Yu.; Kondratiev, V. A.; Schulze, Bert-Wolfgang On the completeness of root functions of elliptic boundary problems in a domain with conical points on the boundary Potsdam Univ. 2004 21 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Informatik und Computational Science OPUS4-12176 Wissenschaftlicher Artikel Coriasco, Sandro; Schulze, Bert-Wolfgang Edge problems on configurations with model cones of different dimensions Elliptic equations on configurations W = W-1 boolean OR (. . .) boolean OR W-N with edge Y and components W-j of different dimension can be treated in the frame of pseudo-differential analysis on manifolds with geometric singularities, here edges. Starting from edge-degenerate operators on Wj, j = 1, . . . , N, we construct an algebra with extra 'transmission' conditions on Y that satisfy an analogue of the Shapiro-Lopatinskij condition. Ellipticity refers to a two-component symbolic hierarchy with an interior and an edge part; the latter one is operator- valued, operating on the union of different dimensional model cones. We construct parametrices within our calculus, where exchange of information between the various components is encoded in Green and Mellin operators that are smoothing on WY. Moreover, we obtain regularity of solutions in weighted edge spaces with asymptotics 2006 Institut für Mathematik OPUS4-12191 Buch (Monographie) Schulze, Bert-Wolfgang Pseudo-differential calculus on Manifolds with geometric singularities Potsdam Univ. 2006 60 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-12180 Wissenschaftlicher Artikel De Donno, Giuseppe; Schulze, Bert-Wolfgang Meromorphic symbolic structures for boundary value problems on manifolds with edges We investigate the ideal of Green and Mellin operators with asymptotics for a manifold with edge-corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges. 2006 10.1002/mana.200310366 Institut für Mathematik OPUS4-12188 Buch (Monographie) Harutjunjan, Gohar; Schulze, Bert-Wolfgang Boundary value problems in weighted edge spaces Potsdam Univ. 2006 21 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-12736 Buch (Monographie) Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich New algebras of boundary value problems for elliptic pseudodifferential operators Potsdam Univ. 2005 80 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-12675 Buch (Monographie) Calvo, D.; Schulze, Bert-Wolfgang Operators on Corner Manifolds with Exit to Infinity Potsdam Univ. 2005 48 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-12916 Buch (Monographie) Kapanadze, David; Schulze, Bert-Wolfgang Boundary-contact Problems for Domains with Edges Singularities Potsdam Univ. 2005 26 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-13046 Buch (Monographie) Martin, Calin-Iulian; Schulze, Bert-Wolfgang The Quantisation of edge symbols Potsdam Univ. 2005 30 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-13411 Wissenschaftlicher Artikel Nazajkinskij, Vladimir E.; Savin, Anton; Sternin, Boris Ju.; Schulze, Bert-Wolfgang On the index of elliptic operators on manifolds with edges Necessary and sufficient conditions for the representation of the index of elliptic operators on manifolds with edges in the form of the sum of homotopy invariants of symbols on the smooth stratum and on the edge are found. An index formula is obtained for elliptic operators on manifolds with edges under symmetry conditions with respect to the edge covariables 2005 Institut für Mathematik OPUS4-13565 Wissenschaftlicher Artikel Dines, Nicoleta; Schulze, Bert-Wolfgang Mellin-edge representations of elliptic operators We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator A(s) in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of A(s) as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices P-s of A(s) interpreted as Mellin-edge representations of P. Copyright (c) 2005 John Wiley & Sons, Ltd 2005 Institut für Physik und Astronomie OPUS4-13758 Wissenschaftlicher Artikel Liu, Xiaochun; Schulze, Bert-Wolfgang Ellipticity on manifolds with edges and boundary Ellipticity of a manifold with edges and boundary is connected to boundary and edge conditions that complete corresponding operators to Fredholm operators between weighted Sobolev spaces. We study a new parameter-dependent calculus of elliptic operators, where the interior symbols have specific properties on the boundary. We construct elliptic operators with a prescribed number of edge conditions and obtain isomorphisms in the scale of edge Sobolev spaces 2005 OPUS4-13740 Wissenschaftlicher Artikel Kytmanov, Alexander M.; Myslivets, Simona; Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich Elliptic problems for the Dolbeault complex The inhomogeneous partial derivative-equation is an inexhaustible source of locally unsolvable equations, subelliptic estimates and other phenomena in partial differential equations. Loosely speaking, for the analysis on complex manifolds with boundary nonelliptic problems are typical rather than elliptic ones. Using explicit integral representations we assign a Fredholm complex to the Dolbeault complex over an arbitrary bounded domain in C-n. (C) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 2005 Institut für Mathematik OPUS4-14104 Buch (Monographie) Calvo, D.; Martin, Calin-Iulian; Schulze, Bert-Wolfgang Symbolic Structures on Corner Manifolds Potsdam Univ. 2004 18 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-14137 Buch (Monographie) Harutjunjan, Gohar; Schulze, Bert-Wolfgang Boundary problems with meromorphic symbols in cylindrical domains Potsdam Univ. 2004 19 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Informatik und Computational Science OPUS4-14287 Buch (Monographie) Harutjunjan, Gohar; Schulze, Bert-Wolfgang The zaremba problem with singular interfaces as a corner boundary value problem Potsdam Univ. 2004 48 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-14313 Buch (Monographie) Jaiani, George V.; Schulze, Bert-Wolfgang Some degenerate elliptic systems and applications to cousped plates Potsdam Univ. 2004 33 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-14278 Buch (Monographie) Schulze, Bert-Wolfgang; Volpato, A. Green operators in the edge calculus Potsdam Univ. 2004 24 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15059 Wissenschaftlicher Artikel Schulze, Bert-Wolfgang; Seiler, Jörg Boundary value problems with global projection conditions Parametrices of elliptic boundary value problems for differential operators belong to an algebra of pseudodifferential operators with the transmission property at the boundary. However, generically, smooth symbols on a manifold with boundary do not have this property, and several interesting applications require a corresponding more general calculus. We introduce here a new algebra of boundary value problems that contains Shapiro-Lopatinskij elliptic as well as global projection conditions; the latter ones are necessary, if an analogue of the Atiyah-Bott obstruction does not vanish. We show that every elliptic operator admits (up to a stabilisation) elliptic conditions of that kind. Corresponding boundary value problems are then Fredholm in adequate scales of spaces. Moreover, we construct parametrices in the calculus. (C) 2003 Elsevier Inc. All rights reserved 2004 Institut für Mathematik OPUS4-15070 Wissenschaftlicher Artikel Rabinovich, Vladimir; Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich Boundary value problems in oscillating cuspidal wedges The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges 2004 OPUS4-15138 Wissenschaftlicher Artikel Harutjunjan, Gohar; Schulze, Bert-Wolfgang Reduction of orders in boundary value problems without transmission property 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 2004 Institut für Mathematik OPUS4-15233 Wissenschaftlicher Artikel Fedosov, Boris; Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich On the index theorem for symplectic orbifolds We give an explicit construction of the trace on the algebra of quantum observables on a symplectiv orbifold and propose an index formula 2004 Institut für Mathematik OPUS4-15195 Wissenschaftlicher Artikel Nazajkinskij, Vladimir E.; Savin, Anton; Sternin, Boris Ju.; Schulze, Bert-Wolfgang Pseudodifferential operators on manifolds with edges 2004 Institut für Mathematik OPUS4-15332 Wissenschaftlicher Artikel Harutjunjan, Gohar; Schulze, Bert-Wolfgang Parametrices of mixed elliptic problems 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 2004 Institut für Mathematik OPUS4-15284 Wissenschaftlicher Artikel Nazajkinskij, Vladimir E.; Savin, Anton; Sternin, Boris Ju.; Schulze, Bert-Wolfgang On the existence of elliptic problems on manifolds with edges 2004 Institut für Mathematik OPUS4-15285 Wissenschaftlicher Artikel Nazajkinskij, Vladimir E.; Savin, Anton; Sternin, Boris Ju.; Schulze, Bert-Wolfgang On the index of differential operators on manifolds with edges 2004 Institut für Mathematik OPUS4-15520 Buch (Monographie) Schulze, Bert-Wolfgang Crack theory with singularities at the boundary Potsdam Univ. 2003 36 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15521 Buch (Monographie) Dines, Nicoleta; Harutjunjan, Gohar; Schulze, Bert-Wolfgang The Zaremba problem in edge sobolev spaces Potsdam Univ. 2003 38 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15618 Buch (Monographie) Schulze, Bert-Wolfgang Toeplitz operators, and ellipticity of boundary value problems with global projection conditions Potsdam Univ. 2003 66 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15623 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Localization (surgery) in elliptic theory Potsdam Univ. 2003 32 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15580 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Elliptic theory on manifolds with nonisolated singularities : 5 Index formulas for elliptic problems on manifolds with edges Potsdam Univ. 2003 84 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15548 Buch (Monographie) Dines, Nicoleta; Schulze, Bert-Wolfgang Melin-edges representations of elliptic operators Potsdam Univ. 2003 43 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15684 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Index defects in elliptic theory Potsdam Univ. 2003 30 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15690 Buch (Monographie) De Donno, G.; Schulze, Bert-Wolfgang Meromorphic symbolic structures for boundary value problems on manifolds with edges Potsdam Univ. 2003 40 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15701 Buch (Monographie) Kapanadze, David; Schulze, Bert-Wolfgang Asymptotics of potentials in the edge calculus Potsdam Univ. 2003 34 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15702 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Pseudodifferential Operators Potsdam Univ. 2003 25 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15703 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Eta Invariant and the Spectral Flow Potsdam Univ. 2003 31 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15655 Buch (Monographie) Fedosov, Boris V.; Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich On index theorem for symplectic orbifolds Potsdam Univ. 2003 44 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15909 Buch (Monographie) Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich Symbol algebra for manifolds with cuspidal singularities Potsdam Univ. 2003 37 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15910 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Manifolds with isolated singularities Potsdam Univ. 2003 38 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-15912 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Elliptic theory on manifolds with edges. I Potsdam Univ. 2003 35 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16698 Buch (Monographie) Harutjunjan, Gohar; Schulze, Bert-Wolfgang Reduction of Orders in Boundary Value Problems without the Transmission Proberty Potsdam Univ. 2002 23 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16718 Buch (Monographie) Nazajkinskij, Vladimir E.; Schulze, Bert-Wolfgang; Sternin, Boris Surgery and the relative index theorem for families of elliptic operators Potsdam Univ. 2002 21 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16869 Buch (Monographie) Maniccia, L.; Schulze, Bert-Wolfgang An algebra of meromorphic corner symbols Potsdam Univ. 2002 50 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16855 Buch (Monographie) Schulze, Bert-Wolfgang; Seiler, Jörg Pseudodifferential boundary value problems with global projection conditions Potsdam Univ. 2002 37 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16894 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Elliptic theory on manifolds with nonisolated singularities : 1 the index of families of cone-degenerate operators Potsdam Univ. 2002 18 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16979 Buch (Monographie) Schulze, Bert-Wolfgang; Seiler, Jörg Edge operators with conditions of toeplitz type Potsdam Univ. 2002 20 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16983 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Elliptic theory on Manifolds with nonisolated singularities : 3 the Spectral flow of Families of conaormal symbols Potsdam Univ. 2002 42 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-16984 Buch (Monographie) Nazajkinskij, Vladimir E.; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Elliptic theory on manifolds with nonisolated singularities : 4 obstructions to elliptic problems on manifolds with edges Potsdam Univ. 2002 21 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-17181 Buch (Monographie) Coriasco, S.; Schulze, Bert-Wolfgang Edge Problems on Configurations with Model Cones of Different Dimensions Potsdam Univ. 2002 41 S. Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell Institut für Mathematik OPUS4-2363 unpublished Kapanadze, David; Schulze, Bert-Wolfgang Boundary value problems on manifolds with exits to infinity We construct a new calculus of boundary value problems with the transmission property on a non-compact smooth manifold with boundary and conical exits to infinity. The symbols are classical both in covariables and variables. The operators are determined by principal symbol tuples modulo operators of lower orders and weights (such remainders are compact in weighted Sobolev spaces). We develop the concept of ellipticity, construct parametrices within the algebra and obtain the Fredholm property. For the existence of Shapiro-Lopatinskij elliptic boundary conditions to a given elliptic operator we prove an analogue of the Atiyah-Bott condition. 2000 urn:nbn:de:kobv:517-opus-25727 Institut für Mathematik OPUS4-2369 unpublished Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich Pseudodifferential operators on manifolds with corners We describe an algebra of pseudodifferential operators on a manifold with corners. 2000 urn:nbn:de:kobv:517-opus-25783 Institut für Mathematik OPUS4-2294 unpublished Schulze, Bert-Wolfgang; Sternin, Boris; Shatalov, Victor On the index of differential operators on manifolds with conical singularities The paper contains the proof of the index formula for manifolds with conical points. For operators subject to an additional condition of spectral symmetry, the index is expressed as the sum of multiplicities of spectral points of the conormal symbol (indicial family) and the integral from the Atiyah-Singer form over the smooth part of the manifold. The obtained formula is illustrated by the example of the Euler operator on a two-dimensional manifold with conical singular point. 1997 urn:nbn:de:kobv:517-opus-24965 Institut für Mathematik OPUS4-2323 unpublished Schulze, Bert-Wolfgang; Nazaikinskii, Vladimir; Sternin, Boris The index of quantized contact transformations on manifolds with conical singularities 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. 1998 urn:nbn:de:kobv:517-opus-25276 Institut für Mathematik OPUS4-2324 unpublished Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris On the invariant index formulas for spectral boundary value problems In the paper we study the possibility to represent the index formula for spectral boundary value problems as a sum of two terms, the first one being homotopy invariant of the principal symbol, while the second depends on the conormal symbol of the problem only. The answer is given in analytical, as well as in topological terms. 1998 urn:nbn:de:kobv:517-opus-25285 Institut für Mathematik OPUS4-2325 unpublished Schulze, Bert-Wolfgang; Nazaikinskii, Vladimir; Sternin, Boris A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators 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. 1998 urn:nbn:de:kobv:517-opus-25296 Institut für Mathematik OPUS4-2329 unpublished Rabinovich, Vladimir; Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich Boundary value problems in cuspidal wedges The paper is devoted to pseudodifferential boundary value problems in domains with cuspidal wedges. Concerning the geometry we even admit a more general behaviour, namely oscillating cuspidal wedges. We show a criterion for the Fredholm property of a boundary value problem and derive estimates of solutions close to edges. 1998 urn:nbn:de:kobv:517-opus-25363 Institut für Mathematik OPUS4-2301 unpublished Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich The Riemann-Roch theorem for manifolds with conical singularities The classical Riemann-Roch theorem is extended to solutions of elliptic equations on manifolds with conical points. 1997 urn:nbn:de:kobv:517-opus-25051 Institut für Mathematik OPUS4-2302 unpublished Schulze, Bert-Wolfgang; Sternin, Boris; Shatalov, Victor Operator algebras on singular manifolds. IV, V 1997 urn:nbn:de:kobv:517-opus-25062 Institut für Mathematik OPUS4-2303 unpublished Nazaikinskii, Vladimir; Schulze, Bert-Wolfgang; Sternin, Boris; Shatalov, Victor A Lefschetz fixed point theorem for manifolds with conical singularities We establish an Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singular points. 1997 urn:nbn:de:kobv:517-opus-25073 Institut für Mathematik OPUS4-2304 unpublished Nazaikinskii, Vladimir; Schulze, Bert-Wolfgang; Sternin, Boris; Shatalov, Victor Quantization of symplectic transformations on manifolds with conical singularities 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. 1997 urn:nbn:de:kobv:517-opus-25084 Institut für Mathematik OPUS4-2305 unpublished Fedosov, Boris; Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich The index of elliptic operators on manifolds with conical points 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. 1997 urn:nbn:de:kobv:517-opus-25096 Institut für Mathematik OPUS4-2307 unpublished Fedosov, Boris; Schulze, Bert-Wolfgang; Tarkhanov, Nikolai Nikolaevich On the index formula for singular surfaces In the preceding paper we proved an explicit index formula for elliptic pseudodifferential operators on a two-dimensional manifold with conical points. Apart from the Atiyah-Singer integral, it contains two additional terms, one of the two being the 'eta' invariant defined by the conormal symbol. In this paper we clarify the meaning of the additional terms for differential operators. 1997 urn:nbn:de:kobv:517-opus-25116 Institut für Mathematik OPUS4-2308 unpublished Schulze, Bert-Wolfgang; Sternin, Boris; Shatalov, Victor On general boundary value problems for elliptic equations We construct a theory of general boundary value problems for differential operators whose symbols do not necessarily satisfy the Atiyah-Bott condition [3] of vanishing of the corresponding obstruction. A condition for these problems to be Fredholm is introduced and the corresponding finiteness theorems are proved. 1997 urn:nbn:de:kobv:517-opus-25138 Institut für Mathematik OPUS4-2309 unpublished Schulze, Bert-Wolfgang; Nazaikinskii, Vladimir; Sternin, Boris; Shatalov, Victor Spectral boundary value problems and elliptic equations on singular manifolds 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. 1997 urn:nbn:de:kobv:517-opus-25147 Institut für Mathematik OPUS4-2465 unpublished Krainer, Thomas; Schulze, Bert-Wolfgang The conormal symbolic structure of corner boundary value problems 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. 2004 urn:nbn:de:kobv:517-opus-26662 Institut für Mathematik OPUS4-2469 unpublished Nazaikinskii, Vladimir; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Differential operators on manifolds with singularities : analysis and topology : Chapter 7: The index problem on manifolds with singularities Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks 2004 urn:nbn:de:kobv:517-opus-26700 Institut für Mathematik OPUS4-2395 unpublished Kapanadze, David; Schulze, Bert-Wolfgang Symbolic calculus for boundary value problems on manifolds with edges 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. 2001 urn:nbn:de:kobv:517-opus-26046 Institut für Mathematik OPUS4-2452 unpublished De Donno, G.; Schulze, Bert-Wolfgang Meromorphic symbolic structures for boundary value problems on manifolds with edges We investigate the ideal of Green and Mellin operators with asymtotics for a manifold with edge-corner singularities and boundary which belongs to the structure of parametrices of elliptic boundary value problems on a configuration with corners whose base manifolds have edges. 2003 urn:nbn:de:kobv:517-opus-26570 Institut für Mathematik OPUS4-2453 unpublished Nazaikinskii, Vladimir; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Differential operators on manifolds with singularities : analysis and topology : Chapter 4: Pseudodifferential operators Contents: Chapter 4: Pseudodifferential Operators 4.1. Preliminary Remarks 4.1.1. Why are pseudodifferential operators needed? 4.1.2. What is a pseudodifferential operator? 4.1.3. What properties should the pseudodifferential calculus possess? 4.2. Classical Pseudodifferential Operators on Smooth Manifolds 4.2.1. Definition of pseudodifferential operators on a manifold 4.2.2. Hörmander's definition of pseudodifferential operators 4.2.3. Basic properties of pseudodifferential operators 4.3. Pseudodifferential Operators in Sections of Hilbert Bundles 4.3.1. Hilbert bundles 4.3.2. Operator-valued symbols. Specific features of the infinite-dimensional case 4.3.3. Symbols of compact fiber variation 4.3.4. Definition of pseudodifferential operators 4.3.5. The composition theorem 4.3.6. Ellipticity 4.3.7. The finiteness theorem 4.4. The Index Theorem 4.4.1. The Atiyah-Singer index theorem 4.4.2. The index theorem for pseudodifferential operators in sections of Hilbert bundles 4.4.3. Proof of the index theorem 4.5. Bibliographical Remarks 2003 urn:nbn:de:kobv:517-opus-26587 Institut für Mathematik OPUS4-2454 unpublished Nazaikinskii, Vladimir; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Differential operators on manifolds with singularities : analysis and topology : Chapter 3: Eta invariant and the spectral flow Contents: Chapter 3: Eta Invariant and the Spectral Flow 3.1. Introduction 3.2. The Classical Spectral Flow 3.2.1. Definition and main properties 3.2.2. The spectral flow formula for periodic families 3.3. The Atiyah-Patodi-Singer Eta Invariant 3.3.1. Definition of the eta invariant 3.3.2. Variation under deformations of the operator 3.3.3. Homotopy invariance. Examples 3.4. The Eta Invariant of Families with Parameter (Melrose's Theory) 3.4.1. A trace on the algebra of parameter-dependent operators 3.4.2. Definition of the Melrose eta invariant 3.4.3. Relationship with the Atiyah-Patodi-Singer eta invariant 3.4.4. Locality of the derivative of the eta invariant. Examples 3.5. The Spectral Flow of Families of Parameter-Dependent Operators 3.5.1. Meromorphic operator functions. Multiplicities of singular points 3.5.2. Definition of the spectral flow 3.6. Higher Spectral Flows 3.6.1. Spectral sections 3.6.2. Spectral flow of homotopies of families of self-adjoint operators 3.6.3. Spectral flow of homotopies of families of parameter-dependent operators 3.7. Bibliographical Remarks 2003 urn:nbn:de:kobv:517-opus-26595 Institut für Mathematik OPUS4-2455 unpublished Schulze, Bert-Wolfgang Crack theory with singularties at the boundary We investigate crack problems, where the crack boundary has conical singularities. Elliptic operators with two-sided elliptc boundary conditions on the plus and minus sides of the crack will be interpreted as elements of a corner algebra of boundary value problems. The corresponding operators will be completed by extra edge conditions on the crack boundary to Fredholm operators in corner Sobolev spaces with double weights, and there are parametrices within the calculus. 2003 urn:nbn:de:kobv:517-opus-26600 Institut für Mathematik OPUS4-2457 unpublished Dines, Nicoleta; Schulze, Bert-Wolfgang Mellin-edge representations of elliptic operators We construct a class of elliptic operators in the edge algebra on a manifold M with an embedded submanifold Y interpreted as an edge. The ellipticity refers to a principal symbolic structure consisting of the standard interior symbol and an operator-valued edge symbol. Given a differential operator A on M for every (sufficiently large) s we construct an associated operator As in the edge calculus. We show that ellipticity of A in the usual sense entails ellipticity of As as an edge operator (up to a discrete set of reals s). Parametrices P of A then correspond to parametrices Ps of As, interpreted as Mellin-edge representations of P. 2003 urn:nbn:de:kobv:517-opus-26627 Institut für Mathematik OPUS4-2460 unpublished Nazaikinskii, Vladimir; Savin, Anton; Schulze, Bert-Wolfgang; Sternin, Boris Differential operators on manifolds with singularities : analysis and topology : Chapter 5: Manifolds with isolated singularities Contents: Chapter 5: Manifolds with Isolated Singularities 5.1. Differential Operators and the Geometry of Singularities 5.1.1. How do isolated singularities arise? Examples 5.1.2. Definition and methods for the description of manifolds with isolated singularities 5.1.3. Bundles. The cotangent bundle 5.2. Asymptotics of Solutions, Function Spaces,Conormal Symbols 5.2.1. Conical singularities 5.2.2. Cuspidal singularities 5.3. A Universal Representation of Degenerate Operators and the Finiteness Theorem 5.3.1. The cylindrical representation 5.3.2. Continuity and compactness 5.3.3. Ellipticity and the finiteness theorem 5.4. Calculus of ΨDO 5.4.1. General ΨDO 5.4.2. The subalgebra of stabilizing ΨDO 5.4.3. Ellipticity and the finiteness theorem 2003 urn:nbn:de:kobv:517-opus-26659 Institut für Mathematik