Overview

The articles in this collection are devoted to various problems in mathematical physics and mathematical analysis, primarily in the fields of spectral theory and the theory of wave processes. The collection is intended for mathematicians sPf>cializing in the fields of mathematical physics, functional analysis, and the theory of differential equations. In addition, it is of some interest to theoretical physicists. The first paper deals with a mixed boundary value problem for a system of elasticity equations, and considers fields in the neighborhood of various wave fronts. The method used permits an estimate of the errors in the Ben-Menahem approximate method. Paper 2 investigates operators in separable Hilbert space given by double integrals of a type defined at the beginning of the paper, and in which integration is understood as the limit of the integral sums of Riemann-stieltjes. In paper 3, the problem of calculation of elastic constants for a laminarly inhomogeneous semi-infinite medium is conSidered, and the uniqueness of the solution of the inverse seismic problem at finite depth proved. The fourth paper gives a detailed account of the results of an earlier paper by the same author, in which he generalized to the three-dimensional case the trace formulas obtained for the one-dimensional Schroedinger operator. Asymptotic estimates of the resolvent kernel and solutions of the scattering problem are given.

Full Product Details

Author:   M. Sh. Birman
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1971 ed.
Volume:   4
Dimensions:   Width: 21.00cm , Height: 0.70cm , Length: 27.90cm
Weight:   0.333kg
ISBN:  

9781468489286

ISBN 10:   1468489283
Pages:   121
Publication Date:   08 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
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Table of Contents

Transition of the Quasi-Levels in the Discrete Spectrum of the Schrödinger Operator under Strong Perturbations of the Potential.- A Criterion for the Existence of the Complete Wave Operators in the Theory of Scattering with Two Spaces.- The Inverse Problem for the Wave Equation with an Unknown Source.- On the Various Formulations of the One-Dimensional Inverse Problem for the Telegraph Equation.- Quantitative Characteristics of Singular Measures.- Spectral Identities and the Trace Formula in the Friedrichs Model.- Perturbation of the Spectrum of the One-Dimensional Self-Adjoint Schrödinger Operator with a Periodic Potential.- The Field of a Point Source Located Outside a Convex Curve.- Criteria for the Boundedness and Complete Continuity of Certain Imbedding Operators.- A Uniqueness Theorem for Functions with Positive Imaginary Part.- Application of the Method of Standard Comparison Problems to Perturbations of the Coulomb Field. The Discrete Spectrum.

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