Operator Calculus and Spectral Theory: Symposium on Operator Calculus and Spectral Theory Lambrecht (Germany) December 1991

✍ Scribed by Thomas P. Branson, Peter B. Gilkey, Bent Ørsted (auth.), Michael Demuth, Bernhard Gramsch, Bert-Wolfgang Schulze (eds.)

• Publisher: Birkhäuser Basel
• Year: 1992
• Tongue: English
• Leaves: 355
• Series: Operator Theory: Advances and Applications 57
• Edition: 1
• Category: Library

✦ Synopsis

Heat equation asymptotics of a generalized Ahlfors Laplacian on a manifold with boundary.- Recurrent versus diffusive quantum behavior for time-dependent Hamiltonians.- Perturbations of spectral measures for Feller operators.- A global approach to the location of quantum resonances.- On estimates for the eigen-values in some elliptic problems.- Quantum scattering with long-range magnetic fields.- Spectral invariance and submultiplicativity for Fréchet algebras with applications to pseudo-differential operators and ?* -quantization.- Décroissance exponentielle des fonctions propres pour l’opérateur de Kac: le cas de la dimension > 1.- Second order perturbations of divergence type operators with a spectral gap.- On the Weyl quantized relativistic Hamiltonian.- Spectral asymptotics for the family of commuting operators.- Pseudo differential operators with negative definite functions as symbol: Applications in probability theory and mathematical physics.- One-dimensional Schrödinger operators with high potential barriers.- General boundary value problems in regions with corners.- Some results for nonlinear equations in cylindrical domains.- Global representation of Langrangian distributions.- Stable asymptotics of the solution to the Dirichlet problem for elliptic equations of second order in domains with angular points or edges.- Maslov operator calculus and non-commutative analysis.- Relative time delay and trace formula for long range perturbations of Laplace operators.- Functional calculus and Fredholm criteria for boundary value problems on noncompact manifolds.- The variable discrete asymptotics of solutions of singular boundary value problems.- Schrödinger operators with arbitrary non-negative potentials.- Abel summability of the series of eigen- and associated functions of the integral and differential operators.- The relativistic oscillator.- On the ratio of odd and even spectral counting functions.- A trace class property of singularly perturbed generalized Schrödinger semi-groups.- Radiation conditions and scattering theory for N-particle Hamiltonians (main ideas of the approach).

✦ Table of Contents

Front Matter....Pages I-XI
Heat equation asymptotics of a generalized Ahlfors Laplacian on a manifold with boundary....Pages 1-13
Recurrent Versus Diffusive Quantum Behavior for Time Dependent Hamiltonians....Pages 15-26
Perturbations of spectral measures for Feller operators....Pages 27-37
A Global Approach to the Location of Quantum Resonances....Pages 39-49
On estimates for the eigen-values in some elliptic problems....Pages 51-60
Quantum Scattering with Long-Range Magnetic Fields....Pages 61-70
Spectral Invariance and Submultiplicativity for Fréchet Algebras with Applications to Pseudo-Differential Operators and Ψ*-Quantization....Pages 71-98
Décroissance exponentielle des fonctions propres pour l’opérateur de Kac: le cas de la dimension >1....Pages 99-115
Second Order Perturbations of Divergence Type Operators with a Spectral Gap....Pages 117-126
On the Weyl Quantized Relativistic Hamiltonian....Pages 127-137
Spectral Asymptotics for the Family of Commuting Operators....Pages 139-148
Pseudo differential operators with negative definite functions as symbol : Applications in probability theory and mathematical physics....Pages 149-161
One dimensional Schrödinger operators with high potential barriers....Pages 163-170
General boundary value problems in region with corners....Pages 171-183
Some Results for Nonlinear Elliptic Equations in Cylindrical Domains....Pages 185-195
Global Representation of Lagrangian Distributions....Pages 197-213
Stable asymptotics of the solution to the Dirichlet problem for elliptic equations of second order in domains with angular points or edges....Pages 215-224
Maslov Operational Calculus and Noncommutative Analysis....Pages 225-243
Relative Time Delay and Trace Formula for Long Range perturbations of Laplace Operator....Pages 245-253
Functional Calculus and Fredholm Criteria for Boundary Value Problems on Noncompact Manifolds....Pages 255-269
The variable discrete asymptotics of solutions of singular boundary value problems....Pages 271-289
Schrödinger Operators with Arbitrary Nonnegative Potentials....Pages 291-306
Abel Summability of the Series of Eigen- and Associated Functions of the Integral and Differential Operators....Pages 307-309
The Relativistic Oscillator....Pages 311-319
On the Ratio of Odd and Even Spectral Counting Functions....Pages 321-328
A Trace Class Property of Singularly Perturbed Generalized Schrödinger Semigroups....Pages 329-347
Radiation Conditions and Scattering Theory for N-Particle Hamiltonians (Main Ideas of the Approach)....Pages 349-360

✦ Subjects

Science, general