Hardcover ISBN:  9780821841068 
Product Code:  ADVSOV/7 
204 pp 
List Price:  $152.00 
MAA Member Price:  $136.80 
AMS Member Price:  $121.60 
Electronic ISBN:  9781470445546 
Product Code:  ADVSOV/7.E 
204 pp 
List Price:  $152.00 
MAA Member Price:  $136.80 
AMS Member Price:  $121.60 

Book DetailsAdvances in Soviet MathematicsVolume: 7; 1991MSC: Primary 34; 35; 45; 47;
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 19891990.
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 largecouplingconstant limit. The starting point here is the opening paper, which is devoted to the important case of a semiinfinite 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. 
Table of Contents

Articles

M. Birman and M. Solomyak  Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations

M. Birman  Discrete spectrum in the gaps of a continuous one for perturbations with large coupling constant

M. Birman and G. Raikov  Discrete spectrum in the gaps for perturbations of the magnetic Schrödinger operator

M. Birman, G. Karadzhov and M. Solomyak  Boundedness conditions and spectrum estimates for the operators $b(X)a(D)$ and their analogs

A. Budylin and V. Buslaev  Reflection operators and their applications to asymptotic investigations of semiclassical integral equations

A. Sobolev  Weyl asymptotics for the discrete spectrum of the perturbed Hill operator

D. Yafaev  On solutions of the Schrödinger equation with radiation conditions at infinity


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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 19891990.
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 largecouplingconstant limit. The starting point here is the opening paper, which is devoted to the important case of a semiinfinite 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.

Articles

M. Birman and M. Solomyak  Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations

M. Birman  Discrete spectrum in the gaps of a continuous one for perturbations with large coupling constant

M. Birman and G. Raikov  Discrete spectrum in the gaps for perturbations of the magnetic Schrödinger operator

M. Birman, G. Karadzhov and M. Solomyak  Boundedness conditions and spectrum estimates for the operators $b(X)a(D)$ and their analogs

A. Budylin and V. Buslaev  Reflection operators and their applications to asymptotic investigations of semiclassical integral equations

A. Sobolev  Weyl asymptotics for the discrete spectrum of the perturbed Hill operator

D. Yafaev  On solutions of the Schrödinger equation with radiation conditions at infinity