TY  - BOOK
A1  - Baumgärtel, Hellmut
A1  - Carey, A.
T1  - Hilbert systems for actions of the circle group
T3  - ESI-Preprint / Erwin-Schröder-Institut für Mathematische Physik, Wien
Y1  - 2000
VL  - 940, 2000
PB  - Erwin-Schröder-Institut für Mathematische Physik
CY  - Wien
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Applications of noncommutative analysis to operator algebras on singular manifolds
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - On a new conformal duality of spherically symmetric space-times
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Rozenblum, G.
T1  - On some analytical index formulas related to operator-valued symbols
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - Long-time asymptotics with geometric singularities in the spatial variables
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - THES
A1  - Gerisch, Magnus
T1  - Doubly weighted degenerate pseudodifferential operators on non-compact domains
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Exactly soluble commutation relations
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential Crack Theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Pseudodifferential operators on manifolds with corners
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Harutjunjan, Gohar
A1  - Schulze, Bert-Wolfgang
A1  - Witt, Ingo
T1  - Boundary value problems in the edge pseudo-differential calculus
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Noncommutative analysis : main ideas, definitions, and theorems
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Klotzek, Benno
T1  - Stetigkeit und Unstetigkeit in der Geometrie
N2  - In diesem Beitrag zum Sammelband MATHEMATIK -INTERDISZIPLINÄR wird zunächst der lange Weg von den frühen Bedürfnissen nach Messung über das Eudoxos-Archimedische Axiom bis hin zu HIBERTs Axiomen der Stetigkeit skizziert. Neben der Präzisierung der Euklidischen Raumvorstellung muss man sich in diesem Zusammenhang mit den Zweifeln an ihrer ausschließlichen Nutzung in den Anwendungen auseinandersetzen: Über die Begriffe des Hausdorffschen und des topologischen Raumes werden die Begriffe der C^r -Mannigfaltigkeit und des Riemannschen bzw. des pseudo-Riemannschen Raumes vorgestellt; somit sind die mathematischen Grundlagen der Speziellen und der Allgemeinen Relativitätstheorie von EINSTEIN begründet, wobei der Anlass - Konstanz der (Vakuum-) Lichtgeschwindigkeit nach MICHELSON - und der Beitrag von MINKOWSKI zur Geometrisierung der Physik gestreift wird. Die klassische nichteuklidische Geometrie von GAUSS, LOBACEVSKIJ und J. BOLYAI wird ebenso erwähnt wie die didaktisch begründete späte Behandlung der Stetigkeit in der Schule. Die schon für die klassische Differentialgeometrie wichtige dreimal stetige Differenzierbarkeit der betrachteten Funktionen ist Anlaß, das 5. Hilbertsche Problem "LIEs Begriff der kontinuierlichen Transformationsgruppe ohne die Annahme der Differenzierbarkeit der die Gruppe definierenden Funktionen" mit seiner positiven Lösung im 20. Jh. ebenso wie die Theorie der diskontinuierlichen oder gar schwach diskontinuierlichen Gruppen zu reflektieren.
Y1  - 2000
SN  - 3-8265- 7061-8
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Slapunov, Aleksandr A.
A1  - Tarchanov, Nikolaj N.
T1  - Green integrals on manifolds with cracks
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
T1  - Eta-invariant and pontrjagin duality in K-theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Baumgärtel, Hellmut
T1  - On a theorem of Ashtekar and Lewandowski in the mathematical framework of canonical quantization in quantum gravity
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Jahnke, Thomas
T1  - Normaler, produktiver Mathematikunterricht
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems on manifolds with exits to infinity
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - Asymtotics of solutions to elliptic equations on manifolds with corners
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Elliptic operators in subspaces
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kneis, Gert
T1  - Mathematik für Wirtschaftswissenschaftler
T3  - Internationale Standardlehrbücher der Wirtschafts- und Sozialwissenschaften
Y1  - 2000
SN  - 3-486-24684-4
PB  - Oldenbourg
CY  - München
ER  - 
TY  - BOOK
A1  - Schrohe, Elmar
T1  - A short introduction to Boutet de Monvel`s calculus
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Hounnon, Hippolyte
T1  - Solid varieties of semirings
Y1  - 2000
SN  - 981-02-4392-8
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Leeratanavalee, Sorasak
T1  - Generalized hypersubstitutions and strongly solid varieties
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Leeratanavalee, Sorasak
T1  - Solid polynomial varieties of semigroups which are definable by identities
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Hounnon, Hippolyte
T1  - Solid varieties of normal ID-semirings
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Jahnke, Thomas
T1  - Die vierte Dimension
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Klein, Markus
A1  - Jecko, Therry
A1  - Wang, Xue Ping
T1  - Existence and semiclassical analysis of the total scattering cross-section for atom-ion collisaions
T3  - Preprint / SFB 288, Differentialgeometrie und Quantenphysik
Y1  - 2000
CY  - Berlin
ER  - 
TY  - BOOK
A1  - Eckhoff, Michael
A1  - Klein, Markus
T1  - Long time behavior of one-dimensional stochastic dynamics
T3  - Preprint / SFB 288, Differentialgeometrie und Quantenphysik
Y1  - 2000
VL  - 455
PB  - TU Berlin, Mathematik Sonderforschungsbereich 288
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Mruczek, Krysztyna
T1  - P-compatible Hypersubstitutions
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Mahdavi, Kazem
T1  - The order of normal form hypersubstitutions of type 2
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Junek, Heinz
A1  - Braunß, Hans-Andreas
A1  - Plewnia, Eckart
T1  - Approximation numbers for polynomials
N2  - Approximation numbers of linear operators are a very useful tool in order to understand the structure and the numerical behaviour of the operators. In this paper, this concept is extended to polynomials on Banach spaces and the approximation numbers of diagonal polynomials are estimated. As a main tool the rank of polynomials as a graduation of finite type polynomials is introduced and studied.
Y1  - 2000
ER  - 
TY  - THES
A1  - Eckhoff, Michael
T1  - Capacity and the low lying spectrum in attractive markov chains
Y1  - 2000
ER  - 
TY  - THES
A1  - Pincus, Richard
T1  - Stochastische Ordnungsrelationen Multivarianter Verteilungsfamilien
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - On the inverse of parabolic systems of partial differential equation of german form in an infinite space-time cylinder : Charpters III - V
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Rätsch, Gunnar
A1  - Schölkopf, B.
A1  - Smola, Alexander J.
A1  - Mika, Sebastian
A1  - Onoda, T.
A1  - Müller, Klaus-Robert
T1  - Robust ensemble learning for data analysis
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
A1  - Witt, Ingo
T1  - Coordinate invarince of the cone algebra with asymptotics
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Eichfeldtheorie
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Allgemeine Relativitätstheorie
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Topologische Aspekte in der Kosmologie
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - On a new conformal duality of spherically symmetric space-times
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Schmidt, Hans-Jürgen
T1  - Editor's note to A. Sakharov
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Dzhunushaliev, Vladimir
A1  - Schmidt, Hans-Jürgen
T1  - Flux Tubes in Weyl Gravity
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Dzhunushaliev, Vladimir
A1  - Schmidt, Hans-Jürgen
T1  - Wormholes and Flux Tubes in the 7D Gravity on the Principal Bundle with SU(2) Gauge Group as the Extra Dimensions
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Dzhunushaliev, Vladimir
A1  - Schmidt, Hans-Jürgen
T1  - New vacuum solutions of conformal Weyl gravity
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Capozziello, Salvatore
A1  - Lambiase, G.
A1  - Schmidt, Hans-Jürgen
T1  - Nonminimal derivative couplings and inflation in generalized theories of gravity
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Bachmann, Michael
A1  - Schmidt, Hans-Jürgen
T1  - Period-doubling bifurcation in strongly anisotropic Bianchi I quantum cosmology
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Denecke, Klaus-Dieter
A1  - Wismath, Shelly
T1  - Hyperidentities and clones
T3  - Algebra, logic and aplications
N2  - The theory of hyperidentities generalises the equational theory of universal algebras and is applicable in several fields of science, especially in computer sciences. This book presents the theory of hyperidentities and its relation to clone identities. The basic concept of hypersubstitution is used to introduce the monoid of hypersubstitutions, hyperidentities, M-hyperidentities, solid and M-solid varieties. This work integrates into a coherent framework many results scattered throughout the literature over the last eighteen years. In addition, the book contains some applications of hyperidentities to the functional completenes problem in multiple-valued logic. The general theory is also extended to partial algberas. The last chapter contains a list of exercises and open problems with suggestions of future work in this area of research.
Y1  - 2000
SN  - 90-5699-235-X
VL  - 14
PB  - Gordon & Breach
CY  - Amsterdam
ER  - 
TY  - JOUR
A1  - Klein, Markus
A1  - Bovier, Anton
A1  - Eckhoff, Michael
A1  - Gayrard, Véronique
T1  - Metastability and small eigenvalues in Markov chains
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Böckmann, Christine
T1  - Evaluation of Multi-spectral Lidar Measurements of the Tropo- and Stratosphere via Modern Mathematical Methods for Inverse III- posed Problems to Determine the Aerosol Size Distribution
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Solid polynomial varieties of semigroups which are definable by identities
Y1  - 2000
SN  - 3-85366-951-4
ER  - 
TY  - BOOK
ED  - Denecke, Klaus-Dieter
ED  - Vogel, Hans-Jürgen
T1  - General algebra and applications : proceedings of the 59th Workshop on General Algebra ; 15th Conference for Young Algebraists, Potsdam 2000
T3  - Berichte aus der Mathematik
Y1  - 2000
SN  - 3-8265-7983-6
PB  - Shaker
CY  - Aachen
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - P-compatible hypersubstitutions and M_P -solid varieties
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Klein, Markus
T1  - Parametrization of periodic weighted operators in terms of gap lengths
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Koppitz, Jörg
T1  - All 2-solid varieties of semigroups
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Fluid, unsolid, and completely unsolid varieties
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Solid varieties of normal ID-semirings
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - THES
A1  - Krainer, Thomas
T1  - Parabolic pseudodifferential operators and long-time asymptotics of solutions
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Koppitz, Jörg
T1  - Essential variables in weak hypersubstitutions
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - Generalized hypersubstitutions and strongly solid varieties
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
A1  - Arworn, Srichan
T1  - Intervals defined by M-solid varieties
Y1  - 2000
SN  - 3-8265- 7983-6
ER  - 
TY  - JOUR
A1  - Denecke, Klaus-Dieter
T1  - The galois correspondence between subvariety lattices and monoids of hypersubstitutions
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Gräter, Joachim
A1  - Klein, Markus
T1  - The Principal Axis Theorem for Holomorphic Functions
Y1  - 2000
ER  - 
TY  - JOUR
A1  - Brungs, Hans
A1  - Gräter, Joachim
T1  - Trees and Valuation Rings
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Sternin, Boris Ju.
T1  - On surgery in elliptic theory
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Nazajkinskij, Vladimir E.
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris Ju.
T1  - Noncommutative Analysis and High-Frequency Asymptotics
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarchanov, Nikolaj N.
T1  - C*-Algebras of SIOïs with Oscillaing Symbols
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kytmanov, Alexander M.
A1  - Myslivec, S.
A1  - Tarchanov, Nikolaj N.
T1  - Removable singularities of CR functions on singular boundaries
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Savin, Anton
A1  - Sternin, Boris Ju.
T1  - Eta invariant and parity conditions
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2000
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Baumgärtel, Hellmut
A1  - Lledó, Fernando
T1  - Dual group actions on C*-algebras and their description by Hilbert extensions
T3  - Preprint / SFB 288, Differentialgeometrie und Quantenphysik
Y1  - 2000
VL  - 445
PB  - Techn. Univ.
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Baumgärtel, Hellmut
T1  - Dual actions on C*-algebras and Hilbert extensions
Y1  - 2000
ER  - 
TY  - BOOK
A1  - Blumenstein, Oswald
A1  - Schachtzabel, Hartmut
A1  - Barsch, Heiner
A1  - Bork, Hans-Rudolf
A1  - Küppers, Udo
T1  - Grundlagen der Geoökologie : Erscheinungen und Prozesse in unserer Umwelt
Y1  - 2000
SN  - 3-540-65280-9
U6  - https://doi.org/10.1007/978-3-642-57062-9
PB  - Springer Berlin Heidelberg
CY  - Berlin, Heidelberg, s.l.
ER  - 
TY  - INPR
A1  - Coriasco, Sandro
A1  - Panarese, Paolo
T1  - Fourier integral operators defined by classical symbols with exit behaviour
N2  - We continue the investigation of the calculus of Fourier Integral Operators (FIOs) in the class of symbols with exit behaviour (SG symbols). Here we analyse what happens when one restricts the choice of amplitude and phase functions to the subclass of the classical SG symbols. It turns out that the main composition theorem, obtained in the environment of general SG classes, has a "classical" counterpart. As an application, we study the Cauchy problem for classical hyperbolic operators of order (1, 1); for such operators we refine the known results about the analogous problem for general SG hyperbolic operators. The material contained here will be used in a forthcoming paper to obtain a Weyl formula for a class of operators defined on manifolds with cylindrical ends, improving the results obtained in [9].
T3  - Preprint - (2000) 24 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25896
ER  - 
TY  - INPR
A1  - Tepoyan, Liparit
T1  - Degenerated operator equations of higher order
N2  - Content: 1 Introduction 2 The one-dimensional case 2.1 The space Wm sub (α) 2.2 Self-adjoint Equation 2.3 Non-selfadjoint Equation 3 Operator Equation
T3  - Preprint - (2000) 23 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25888
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Sternin, Boris
T1  - On surgery in elliptic theory
N2  - We prove a general theorem on the behavior of the relative index under surgery for a wide class of Fredholm operators, including relative index theorems for elliptic operators due to Gromov-Lawson, Anghel, Teleman, Booß-Bavnbek-Wojciechowski, et al. as special cases. In conjunction with additional conditions (like symmetry conditions), this theorem permits one to compute the analytical index of a given operator. In particular, we obtain new index formulas for elliptic pseudodifferential operators and quantized canonical transformations on manifolds with conical singularities.
T3  - Preprint - (2000) 22 
KW  - elliptic operators
KW  - index theory
KW  - surgery
KW  - relative index
KW  - manifold with singularities
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25873
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Eta invariant and parity conditions
N2  - We give a formula for the η-invariant of odd order operators on even-dimensional manifolds, and for even order operators on odd-dimensional manifolds. Geometric second order operators are found with nontrivial η-invariants. This solves a problem posed by P. Gilkey.
T3  - Preprint - (2000) 21 
KW  - eta invariant
KW  - parity conditions
KW  - K-theory
KW  - linking coefficients
KW  - Dirac operators
KW  - spectral flow
KW  - elliptic operators
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25869
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Chapter 11: Noncommutative analysis and high-frequency asymptotics
N2  - Content: Chapter 11: Noncommutative Analysis and High-Frequency Asymptotics 11.1 Statement of the Problem 11.2 Mixed Asymptotics: the General Scheme 11.3 The Asymptotic Solution of Main Problem 11.4 Analysis of the Asymptotic Solution
T3  - Preprint - (2000) 20 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25857
ER  - 
TY  - INPR
A1  - Rabinovich, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - C*-algebras of ISO's with oscillating symbols
N2  - For a domain D subset of IRn with singular points on the boundary and a weight function ω infinitely differentiable away from the singularpoints in D, we consider a C*-algebra G (D; ω) of operators acting in the weighted space L² (D, ω). It is generated by the operators XD F-¹ σ F XD where σ is a homogeneous function. We show that the techniques of limit operators apply to define a symbol algebra for G (D; ω). When combined with the local principle, this leads to describing the Fredholm operators in G (D; ω).
T3  - Preprint - (2000) 19 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25847
ER  - 
TY  - INPR
A1  - Kytmanov, Aleksandr
A1  - Myslivets, Simona
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Removable singularities of CR functions on singular boundaries
N2  - The problem of analytic representation of integrable CR functions on hypersurfaces with singularities is treated. The nature o singularities does not matter while the set of singularities has surface measure zero. For simple singularities like cuspidal points, edges, corners, etc., also the behaviour of representing analytic functions near singular points is studied.
T3  - Preprint - (2000) 18 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25836
ER  - 
TY  - INPR
A1  - Krainer, Thomas
A1  - Schulze, Bert-Wolfgang
T1  - Long-time asymptotics with geometric singularities in the spatial variables
N2  - Content: Introduction 1 Anisotropic operators in a cylinder with a conical base 1.1 Manifolds with conical singularities and opertors of Fuchs type 1.2 Typical operators and symbol structures 2 Weighted wedge Sobolev spaces and edge asymptotics 2.1 Discrete edge asymptotics 2.2 Continuos edge asymptotics with discrete limit at infinity 2.3 Calculus with operator valued symbols 3 Corner asymptotics at infinity 3.1 The structure of singular functions 3.2 Operators with trace and potential conditions 3.3 Asymptotics and (anisotropic) elliptic regularity
T3  - Preprint - (2000) 17 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25824
ER  - 
TY  - INPR
A1  - Rozenblum, G.
T1  - On some analytical index formulas related to operator-valued symbols
N2  - For several classes of pseudodifferential operators with operator-valued symbol analytic index formulas are found. The common feature is that uasual index formulas are not valid for these operators. Applications are given to pseudodifferential operators on singular manifolds.
T3  - Preprint - (2000) 16 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25811
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Chapter 3: Applications of noncommutative analysis to operator algebras on singular manifolds
N2  - Content: Chapter 3: Applications of Noncommutative Analysis to Operator Algebras on Singular Manifolds 3.1 Statement of the problem 3.2 Operators on the Model Cone 3.3 Operators on the Model Cusp of Order k 3.4 An Application to the Construction of Regularizers and Proof of the Finiteness Theorem
T3  - Preprint - (2000) 15 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25801
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Chapter 2: Exactly soluble commutation relations (The simplest class of classical mechanics)
N2  - Content: Chapter 2: Exactly SolubleCommutation Relations (The Simplest Class of Classical Mechanics) 2.1 Some examples 2.2 Lie commutation relations 2.3 Non-Lie (nonlinear) commutation relations
T3  - Preprint - (2000) 14 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25796
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Pseudodifferential operators on manifolds with corners
N2  - We describe an algebra of pseudodifferential operators on a manifold with corners.
T3  - Preprint - (2000) 13 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25783
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Green integrals on manifolds with cracks
N2  - We prove the existence of a limit in Hm(D) of iterations of a double layer potential constructed from the Hodge parametrix on a smooth compact manifold with boundary, X, and a crack S ⊂ ∂D, D being a domain in X. Using this result we obtain formulas for Sobolev solutions to the Cauchy problem in D with data on S, for an elliptic operator A of order m ≥ 1, whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of the double layer potential. A similar regularisation is constructed also for a mixed problem in D.
T3  - Preprint - (2000) 12 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25777
ER  - 
TY  - INPR
A1  - Nazaikinskii, Vladimir
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Quantization methods in differential equations : Part II: Quantization by the method of ordered operators (Noncommutative Analysis) : Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems
N2  - Content: 0.1 Preliminary Remarks Chapter 1: Noncommutative Analysis: Main Ideas, Definitions, and Theorems 1.1 Functions of One Operator (Functional Calculi) 1.2 Functions of Several Operators 1.3 Main Formulas of Operator Calculus 1.4 Main Tools of Noncommutative Analysis 1.5 Composition Laws and Ordered Representations
T3  - Preprint - (2000) 11 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25762
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential crack theory
N2  - Crack problems are regarded as elements in a pseudo-differential algbra, where the two sdes int S± of the crack S are treated as interior boundaries and the boundary Y of the crack as an edge singularity. We employ the pseudo-differential calculus of boundary value problems with the transmission property near int S± and the edge pseudo-differential calculus (in a variant with Douglis-Nirenberg orders) to construct parametrices od elliptic crack problems (with extra trace and potential conditions along Y) and to characterise asymptotics of solutions near Y (expressed in the framework of continuous asymptotics). Our operator algebra with boundary and edge symbols contains new weight and order conventions that are necessary also for the more general calculus on manifolds with boundary and edges.
T3  - Preprint - (2000) 09 
KW  - Crack theory
KW  - pseudo-differential boundary value problems
KW  - operator algebras on manifolds with singularities
KW  - conormal asymptotics
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25759
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Sternin, Boris
T1  - Eta-invariant and Pontrjagin duality in K-theory
N2  - The topological significance of the spectral Atiyah-Patodi-Singer η-invariant is investigated. We show that twice the fractional part of the invariant is computed by the linking pairing in K-theory with the orientation bundle of the manifold. The Pontrjagin duality implies the nondegeneracy of the linking form. An example of a nontrivial fractional part for an even-order operator is presented.
T3  - Preprint - (2000) 08 
KW  - eta-invariant
KW  - K-theory
KW  - Pontrjagin duality
KW  - linking coefficients
KW  - Atiyah-Patodi-Singer theory
KW  - modulo n index
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25747
ER  - 
TY  - INPR
A1  - Myslivets, Simona
T1  - On the boundary behaviour of the logarithmic residue integral
N2  - A formula of multidimensional logarithmic residue is proved for holomorphic maps with zeroes on the boundary of a bounded domain in Cn.
T3  - Preprint - (2000) 07 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25733
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems on manifolds with exits to infinity
N2  - 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.
T3  - Preprint - (2000) 06 
KW  - pseudo-differentialboundary value problems
KW  - elliptic operators on non-compact manifolds
KW  - Atiyah-Bott condition
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25727
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Asymptotics of solutions to elliptic equatons on manifolds with corners
N2  - We show an explicit link between the nature of a singular point and behaviour of the coefficients of the equation, under which formal asymptotic expansions are still available.
T3  - Preprint - (2000) 05 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25716
ER  - 
TY  - INPR
A1  - Savin, Anton
A1  - Schulze, Bert-Wolfgang
A1  - Sternin, Boris
T1  - Elliptic operators in subspaces
N2  - We construct elliptic theory in the subspaces, determined by pseudodifferential projections. The finiteness theorem as well as index formula are obtained for elliptic operators acting in the subspaces. Topological (K-theoretic) aspects of the theory are studied in detail.
T3  - Preprint - (2000) 04 
KW  - pseudodifferential subspaces
KW  - elliptic operators in subspaces
KW  - Fredholm property
KW  - index
KW  - K-theory
KW  - problem of classification
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25701
ER  - 
TY  - INPR
A1  - Schrohe, Elmar
T1  - A short introduction to Boutet de Monvel's calculus
N2  - This paper provides an introduction to Boutet de Monvel's calculus on the half-space IRn (positiv) in the framework of a pseudodifferential calculus with operator-valued symbols.
T3  - Preprint - (2000) 03 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25696
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
T1  - On Iterations of double layer potentials
N2  - We prove the existence of Hp(D)-limit of iterations of double layer potentials constructed with the use of Hodge parametrix on a smooth compact manifold X, D being an open connected subset of X. This limit gives us an orthogonal projection from Sobolev space Hp(D) to a closed subspace of Hp(D)-solutions of an elliptic operator P of order p ≥ 1. Using this result we obtain formulae for Sobolev solutions to the equation Pu = f in D whenever these solutions exist. This representation involves the sum of a series whose terms are iterations of double layer potentials. Similar regularization is constructed also for a P-Neumann problem in D.
T3  - Preprint - (2000) 02 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25687
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
A1  - Witt, Ingo
T1  - Coordinate invariance of the cone algebra with asymptotics
N2  - The cone algebra with discrete asymptotics on a manifold with conical singularities is shown to be invariant under natural coordinate changes, where the symbol structure (i.e., the Fuchsian interior symbol, conormal symbols of all orders) follows a corresponding transformation rule.
T3  - Preprint - (2000) 01 
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25671
ER  -