Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations

Front Cover
M. Sh Birman, Michail Š Birman
American Mathematical Soc., 1991 - Differential equations - 204 pages

The Leningrad Seminar on mathematical physics, begun in 1947 by V. I. Smirnov and now run by O. A. Ladyzhenskaya, is sponsored by Leningrad University and the Leningrad Branch of the Steklov Mathematical Institute of the Academy of Sciences of the USSR. The main topics of the seminar center on the theory of boundary value problems and related questions of analysis and mathematical physics. This volume contains adaptations of lectures presented at the seminar during the academic year 1989-1990.

For the most part, the papers are devoted to investigations of the spectrum of the Schrödinger operator (or its generalizations) perturbed by some relatively compact operator. The book studies the discrete spectrum that emerges in the spectral gaps of the nonperturbed operator, and considers the corresponding estimates and asymptotic formulas for spectrum distribution functions in the large-coupling-constant limit. The starting point here is the opening paper, which is devoted to the important case of a semi-infinite gap. The book also covers the case of inner gaps, related questions in the theory of functions, and an integral equation with difference kernel on a finite interval. The collection concludes with a paper focusing on the classical problem of constructing scattering theory for the Schrödinger operator with potential decreasing faster than the Coulomb potential

 

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Volume 7
2
SH BIRMAN AND M Z SOLOMYAK
8
fundamental estimates and interpolation
14
5 The case 21 d Spectrum estimates to the left of a
27
A noninterpolation approach
33
8 Examples of explicit asymptotic formulas
42
Magnetic Schrödinger operator Periodic operator
49
Discrete Spectrum in the Gaps of a Continuous One for Perturbations
54
Mathematics Subject Classification Primary 35J10 35P20
57
Discrete Spectrum in the Gaps for Perturbations of the Magnetic
73
Reflection Operators and Their Applications to Asymptotic
107
Weyl Asymptotics for the Discrete Spectrum of the Perturbed Hill
159
On Solutions of the Schrödinger Equation with Radiation Conditions
179
Copyright

Common terms and phrases

Bibliographic information