Overview

This work contains the contributions to the conference on ""Partial Differential Equations"" held in Holzhau in July 1994. Topics covered include: hyperbolic operators with double characteristics or with degeneracies; quasi-elliptic operators; spectral theory for elliptic operators; eta-invariant; singular configurations and asymptotics; Bergman-kernal; attractors of non-autonomous evolution equations; pseudo-differential operators; approximations and stability problems for elliptic operators; and operator determinants. In spectral theory adiabatic and semiclassical limits, Dirichlet decoupling and domain perturbations, capacity of obstacles, limiting absorption problems, N-body scattering and number of bound states are considered. Schrodinger operators are studied with magnetic fields, with random and with many-body potentials, and for nonlinear problems. In semigroup theory, the Feller property, errors for product formulas, fractional powers of generators and functional integration for relativistic semigroups are analyzed.

Full Product Details

Author:   Michael Demuth ,  Bert-Wolfgang Schulze
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1995 ed.
Volume:   78
Weight:   0.892kg
ISBN:  

9783764352080

ISBN 10:   3764352086
Pages:   430
Publication Date:   01 May 1995
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
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Table of Contents

A remark on coercive forms and associated semigroups.- Domain perturbation for the first eigenvalue of the Dirichlet Schrödinger operator.- Geometric transition for a class of hyperbolic operators with double characteristics.- Multi-quasi-elliptic operators in ?n.- Real analogue of the Bergman kernel.- Attractors of non-autonomous evolution equations with translation-compact symbols.- Localization for 2-dimensional random Schrödinger operators with magnetic fields.- Some problems of calculus of variations in infinite dimensions.- Finite capacities in spectral theory.- Classical N-body scattering.- Quantum Fermi accelerators with pure-point quasi-spectrum.- On moments of negative eigenvalues of an elliptic operator.- Magnetic Lieb-Thirring inequalities and stochastic oscillatory integrals.- On the trace density in deformation quantization.- The stationary phase method with remainder estimate as dimension of the space goes to infinity.- The eta invariant, equivariant spin bordism, and metrics of positive scalar curvature.- Generalized Strichartz inequalities for the wave equation.- Around the transfer operator and the Totter-Kato formula.- Bands and gaps for periodic magnetic Hamiltonians.- H?-calculus for second order elliptic operators in divergence form.- Path integral for the relativistic Schrödinger semigroup.- Semiclassical spectral asymptotics and multiparticle quantum theory.- Product formulas and error estimates.- On inequalities for the bound states of Schrödinger operators.- Some examples of two-term spectral asymptotics for sets with fractal boundary.- Estimates for Fourier transforms of surface-carried densities on surfaces with singular points.- On adiabatic reduction theory.- Recurrence for fractional powers of diffusion operators in terms ofvolume-growth.- Band spectrum for Schrödinger operators with strong periodic magnetic fields.- Mellin pseudodifferential operators with operator symbols and its applications.- Hypoellipticity of certain differential operators with degeneration of infinite order.- On approximation of solutions of elliptic boundary value problems for Petrovskii elliptic systems by linear combinations of fundamental solutions.- The reduced wave operator with two unbounded media.- Mellin quantization in the cone calculus for Boutet de Monnvel’s algebra.- Transmission algebras on singular spaces with components of different dimensions.- On approximation by solutions of non-local elliptic problems.- A stability set in the Cauchy problem for elliptic systems.- Discrete spectrum asymptotics for the Schrödinger operator.- Convergence of Scbrödjnger operators on varying domains.- Localization for the Poisson model.- Systems of partial differential equations for a class of operator determinants.- Absorption semigroups, Feller property, and Kato class.- Gaussian estimates and analytic semigroups.- New channels of scattering for long-range potentials.- Participants.- Talks.

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