TY - INPR A1 - Schulze, Bert-Wolfgang T1 - The structure of operators on manifolds with polyhedral singularities N2 - We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities. T3 - Preprint - (2006) 05 Y1 - 2006 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30099 ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - Operators with symbol hierarchies and iterated asymptotics N2 - Contents: Introduction 1 Edge calculus with parameters 1.1 Cone asymptotics and Green symbols 1.2 Mellin edge symbols 1.3 The edge symbol algebra 1.4 Operators on a manifold with edges 2 Corner symbols and iterated asymptotics 2.1 Holomorphic corner symbols 2.2 Meromorphic corner symbols and ellipicity 2.3 Weighted corner Sobolev spaces 2.4 Iterated asymptotics 3 The edge corner algebra with trace and potential conditions 3.1 Green corner operators 3.2 Smoothing Mellin corner operators 3.3 The edge corner algebra 3.4 Ellipicity and regularity with asymptotics 3.5 Examples and remarks T3 - Preprint - (2001) 10 Y1 - 2001 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25948 ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - Toeplitz operators, and ellipticity of boundary value problems with global projection conditions N2 - Ellipticity of (pseudo-) differential operators A on a compact manifold X with boundary (or with edges) Y is connected with boundary (or edge) conditions of trace and potential type, formulated in terms of global projections on Y together with an additional symbolic structure. This gives rise to operator block matrices A with A in the upper left corner. We study an algebra of such operators, where ellipticity is equivalent to the Fredhom property in suitable scales of spaces: Sobolev spaces on X plus closed subspaces of Sobolev spaces on Y which are the range of corresponding pseudo-differential projections. Moreover, we express parametrices of elliptic elements within our algebra and discuss spectral boundary value problems for differential operators. T3 - Preprint - (2003) 03 Y1 - 2003 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26510 ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - Operator algebras with symbol hierarchies on manifolds with singularities N2 - 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. T3 - Preprint - (1999) 30 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25647 ER - TY - INPR A1 - Schulze, Bert-Wolfgang T1 - An algebra of boundary value problems not requiring Shapiro-Lopatinskil conditions N2 - 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. T3 - Preprint - (1999) 24 Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25596 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir E. A1 - Sternin, Boris T1 - On the homotopy classification of elliptic operators on manifolds with singularities N2 - 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. T3 - Preprint - (1999) 21 KW - elliptic operators KW - homotopy classification KW - manifold with singularities KW - Atiyah-Singer theorem Y1 - 1999 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25574 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - The index of quantized contact transformations on manifolds with conical singularities N2 - 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. T3 - Preprint - (1998) 16 KW - manifolds with conical singularities KW - contact transformations KW - quantization KW - ellipticity KW - Fredholm operators KW - regularizers KW - index formulas Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25276 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris T1 - A semiclassical quantization on manifolds with singularities and the Lefschetz Formula for Elliptic Operators N2 - 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. T3 - Preprint - (1998) 19 KW - elliptic operator KW - Fredholm property KW - conical singularities KW - pseudodiferential operators KW - Lefschetz fixed point formula KW - regularizer Y1 - 1998 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25296 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Nazaikinskii, Vladimir A1 - Sternin, Boris A1 - Shatalov, Victor T1 - Spectral boundary value problems and elliptic equations on singular manifolds N2 - 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. T3 - Preprint - (1997) 36 KW - APS problem KW - spectral resolution KW - nonhomogeneous boundary value problems KW - Fredholm property Y1 - 1997 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25147 ER - TY - INPR A1 - Schulze, Bert-Wolfgang A1 - Qin, Yuming T1 - Uniform compact attractors for a nonlinear non-autonomous equation of viscoelasticity N2 - In this paper we establish the regularity, exponential stability of global (weak) solutions and existence of uniform compact attractors of semiprocesses, which are generated by the global solutions, of a two-parameter family of operators for the nonlinear 1-d non-autonomous viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions. T3 - Preprint - (2005) 13 KW - exponential stability KW - semiprocess KW - absorbing set KW - C0−semigroup KW - uniform compact attractor Y1 - 2005 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29892 ER -