Birman M. Sh. (Ed.) Estimates and Asymptotics for Discrete Spectra of Integral and Differential Equations

Providence: American Mathematical Society. - 1991. - 204 p. (Advances in SOVIET MATHEMATICS. Volume 7) The papers of this collections contain adapted expositions of a series of talks on spectral theory given to the Leningrad Seminar on Mathematical Physics in the academic year of 1989-.
90. A few words about the seminar itself. This is a city seminar (based on Leningrad University and LOMI, the Leningrad Branch of the Steklov Mathematical Institute of the Academy of Sciences of the USSR) on the theory of boundary value problems and related questions of analysis and mathematical physics..
For the most part, the papers in this collection are devoted to investigations of the spectrum of the Schrodinger operator (or its generalizations) perturbed by some relatively compact operator. The discrete spectrum that emerges in the spectral gaps of the nonperturbed operator is studied. The corresponding estimates and asymptotic formulas for spectrum distribution functions are considered in the large-coupling-constant limit. The collection was supposed to promptly give an account of current re-search in spectral theory by participants of the seminar. The technical stage of the work on it has taken more time than was expected.Editor’s Preface.
Estimates for the Number of Negative Eigenvalues of the Schrodinger Operator and Its Generalizations.
Discrete Spectrum in the Gaps of a Continuous One for Perturbations with Large Coupling Constant.
Discrete Spectrum in the Gaps for Perturbations of the Magnetic Schrodinger Operator.
Boundedness Conditions and Spectrum Estimates for the Operators b(X)a(D) and Their Analogs and Reflection Operators and Their Applications to Asymptotic.
Investigations of Semiclassical Integral Equations A.
Weyl Asymptotics for the Discrete Spectrum of the Perturbed Hill Operator.
On Solutions of the Schrodinger Equation with Radiation Conditions at Infinity.