@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} } @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{NazajkinskijSterninSchulze1999, author = {Nazajkinskij, Vladimir E. and Sternin, Boris Ju. and Schulze, Bert-Wolfgang}, title = {The index of quantized contact transformations on manifolds with conical singularities}, issn = {0002-3264}, year = {1999}, language = {en} } @article{FedosovSchulzeTarchanov1999, author = {Fedosov, Boris V. and Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {The index of elliptic operators on manifolds with conical points}, year = {1999}, language = {en} } @book{SchulzeSavinSternin1999, author = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris Ju.}, title = {The homotopy classification and the index of boundary value problems for general elliptic operators}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {27 S. : graph. Darst.}, year = {1999}, language = {en} } @unpublished{SchulzeSterninSavin1999, author = {Schulze, Bert-Wolfgang and Sternin, Boris and Savin, Anton}, title = {The homotopy classification and the index of boundary value problems for general elliptic operators}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25568}, year = {1999}, abstract = {We give the homotopy classification and compute the index of boundary value problems for elliptic equations. The classical case of operators that satisfy the Atiyah-Bott condition is studied first. We also consider the general case of boundary value problems for operators that do not necessarily satisfy the Atiyah-Bott condition.}, language = {en} } @article{NazajkinskijSchulzeSterninetal.1999, author = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {The Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities}, year = {1999}, language = {en} } @article{NazajkinskijSchulzeSterninetal.1999, author = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {The Atiyah-Bott-Lefschetz formula for elliptic operators on manifolds with conical singularities}, issn = {0002-3264}, year = {1999}, language = {en} } @article{NazajkinskijSchulzeSterninetal.1999, author = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Spectral boundary value problems and elliptic equations on manifolds with singularities}, issn = {0002-3264}, year = {1999}, language = {en} } @unpublished{SchulzeShlapunovTarkhanov1999, author = {Schulze, Bert-Wolfgang and Shlapunov, Alexander and Tarkhanov, Nikolai Nikolaevich}, title = {Regularisation of mixed boundary problems}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25454}, year = {1999}, abstract = {We show an application of the spectral theorem in constructing approximate solutions of mixed boundary value problems for elliptic equations.}, language = {en} } @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} } @article{NazajkinskijSchulzeSterninetal.1999, author = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {Quantizational of canonical transformations on manifolds with conical singularities}, issn = {0002-3264}, year = {1999}, language = {en} } @book{NazajkinskijSchulzeSternin1999, author = {Nazajkinskij, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris Ju.}, title = {Quantization of Lagrangian modules}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {27 S.}, year = {1999}, language = {en} } @unpublished{NazaikinskiiSchulzeSternin1999, author = {Nazaikinskii, Vladimir E. and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Quantization methods in differential equations : Chapter 2: Quantization of Lagrangian modules}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25582}, year = {1999}, abstract = {In this chapter we use the wave packet transform described in Chapter 1 to quantize extended classical states represented by so-called Lagrangian sumbanifolds of the phase space. Functions on a Lagrangian manifold form a module over the ring of classical Hamiltonian functions on the phase space (with respect to pointwise multiplication). The quantization procedure intertwines this multiplication with the action of the corresponding quantum Hamiltonians; hence we speak of quantization of Lagrangian modules. The semiclassical states obtained by this quantization procedure provide asymptotic solutions to differential equations with a small parameter. Locally, such solutions can be represented by WKB elements. Global solutions are given by Maslov's canonical operator [2]; also see, e.g., [3] and the references therein. Here the canonical operator is obtained in the framework of the universal quantization procedure provided by the wave packet transform. This procedure was suggested in [4] (see also the references there) and further developed in [5]; our exposition is in the spirit of these papers. Some further bibliographical remarks can be found in the beginning of Chapter 1.}, language = {en} } @unpublished{NazaikinskiiSchulzeSternin1999, author = {Nazaikinskii, Vladimir and Schulze, Bert-Wolfgang and Sternin, Boris}, title = {Quantization and the wave packet transform}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25447}, year = {1999}, language = {en} } @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 = {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{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} } @unpublished{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Operator algebras with symbol hierarchies on manifolds with singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25647}, year = {1999}, abstract = {Problems for elliptic partial differential equations on manifolds M with singularities M' (here with piece-wise smooth geometry)are studied in terms of pseudo-differential algebras with hierarchies of symbols that consist of scalar and operator-valued components. Classical boundary value problems (with or without the transmission property) belong to the examples. They are a model for operator algebras on manifolds M with higher "polyhedral" singularities. The operators are block matrices that have upper left corners containing the pseudo-differential operators on the regular M\M' (plus certain Mellin and Green summands) and are degenerate (in streched coordinates) in a typical way near M'. By definition M' is again a manifold with singularities. The same is true of M'', and so on. The block matrices consist of trace, potential and Mellin and Green operators, acting between weighted Sobolev spaces on M(j) and M(k), with 0 ≤ j, k ≤ ord M; here M(0) denotes M, M(1) denotes M', etc. We generate these algebras, including their symbol hierarchies, by iterating so-called "edgifications" and "conifications" os algebras that have already been constructed, and we study ellipicity, parametrics and Fredholm property within these algebras.}, language = {en} } @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{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{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} } @unpublished{SchulzeNazaikinskiiSternin1999, author = {Schulze, Bert-Wolfgang and Nazaikinskii, Vladimir E. and Sternin, Boris}, title = {On the homotopy classification of elliptic operators on manifolds with singularities}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25574}, year = {1999}, abstract = {We study the homotopy classification of elliptic operators on manifolds with singularities and establish necessary and sufficient conditions under which the classification splits into terms corresponding to the principal symbol and the conormal symbol.}, language = {en} } @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} } @article{SchulzeSterninSatalov1999, author = {Schulze, Bert-Wolfgang and Sternin, Boris Ju. and Satalov, Viktor E.}, title = {On boundary value problems for elliptic equations}, issn = {0002-3264}, year = {1999}, language = {en} } @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{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {Iterated asymptotics on corner manifolds}, 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} } @article{SchulzeTarchanov1999, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Ellipticity and parametrices on manifolds with cuspidal edges}, year = {1999}, language = {en} } @unpublished{SchulzeTarkhanov1999, author = {Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Ellipticity and parametrices on manifolds with caspidal edges}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25411}, year = {1999}, language = {en} } @unpublished{SchulzeSavinSternin1999, author = {Schulze, Bert-Wolfgang and Savin, Anton and Sternin, Boris}, title = {Elliptic operators in subspaces and the eta invariant}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25496}, year = {1999}, abstract = {The paper deals with the calculation of the fractional part of the η-invariant for elliptic self-adjoint operators in topological terms. The method used to obtain the corresponding formula is based on the index theorem for elliptic operators in subspaces obtained in [1], [2]. It also utilizes K-theory with coefficients Zsub(n). In particular, it is shown that the group K(T*M,Zsub(n)) is realized by elliptic operators (symbols) acting in appropriate subspaces.}, language = {en} } @article{SchulzeTarchanov1999, author = {Schulze, Bert-Wolfgang and Tarchanov, Nikolaj N.}, title = {Elliptic complexes of pseudodifferential operators on manifolds with edges}, year = {1999}, language = {en} } @unpublished{SchroheSchulze1999, author = {Schrohe, Elmar and Schulze, Bert-Wolfgang}, title = {Edge-degenerate boundary value problems on cones}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25436}, year = {1999}, abstract = {We consider edge-degenerate families of pseudodifferential boundary value problems on a semi-infinite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near infinity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.}, 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{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} } @unpublished{RabinovichSchulzeTarkhanov1999, author = {Rabinovich, Vladimir and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {Boundary value problems in domains with corners}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25552}, year = {1999}, abstract = {We describe Fredholm boundary value problems for differential equations in domains with intersecting cuspidal edges on the boundary.}, language = {en} } @unpublished{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25596}, year = {1999}, abstract = {We construct an algebra of pseudo-differential boundary value problems that contains the classical Shapiro-Lopatinskij elliptic problems as well as all differential elliptic problems of Dirac type with APS boundary conditions, together with their parametrices. Global pseudo-differential projections on the boundary are used to define ellipticity and to show the Fredholm property in suitable scales of spaces.}, language = {en} } @book{Schulze1999, author = {Schulze, Bert-Wolfgang}, title = {An algebra of boundary value problems not requiring Shapiro-Lopatinskij conditions}, series = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, journal = {Preprint / Universit{\"a}t Potsdam, Institut f{\"u}r Mathematik, Arbeitsgruppe Partiell}, publisher = {Univ.}, address = {Potsdam}, issn = {1437-739X}, pages = {31 S.}, year = {1999}, language = {en} } @unpublished{FedosovSchulzeTarkhanov1999, author = {Fedosov, Boris and Schulze, Bert-Wolfgang and Tarkhanov, Nikolai Nikolaevich}, title = {A general index formula on tropic manifolds with conical points}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-25501}, year = {1999}, abstract = {We solve the index problem for general elliptic pseudodifferential operators on toric manifolds with conical points.}, language = {en} }