This volume is dedicated to Professor M. Sh. Birman in honor of his eightieth birthday. It contains original articles in spectral and scattering theory of differential operators, in particular, Schrödinger operators, and in homogenization theory. All articles are written by members of M. Sh. Birman's research group who are affiliated with different universities all over the world. A specific feature of the majority of the papers is a combination of traditional methods with new modern ideas.

Readership

Graduate students and research mathematicians interested theory of differential operators.

Table of Contents

• M. Solomyak and T. Suslina -- On the scientific work of M. Sh. Birman in 1998-2007
• T. Suslina and D. Yafaev -- Continuation of the list of publications of M. Sh. Birman
• M. Sh. Birman -- Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions
• V. S. Buslaev and S. B. Levin -- Asymptotic behavior of the eigenfunctions of many-particle Schrödinger operator. I. One-dimensional particles
• M. N. Demchenko and N. D. Filonov -- Spectral asymptotics of the Maxwell operator on Lipschitz manifolds with boundary
• R. L. Frank and A. Laptev -- Spectral inequalities for Schrödinger operators with surface potentials
• L. Friedlander and M. Solomyak -- On the spectrum of the Dirichlet Laplacian in a narrow infinite strip
• E. Korotyaev and A. Kutsenko -- Lyapunov functions of periodic matrix-valued Jacobi operators
• A. Laptev and A. V. Sobolev -- Hardy inequalities for simply connected planar domains
• A. Pushnitski -- The spectral flow, the Fredholm index, and the spectral shift function
• G. Raikov -- On the spectrum of a translationally invariant Pauli operator
• G. Rozenblum and A. V. Sobolev -- Discrete spectrum distribution of the Landau operator perturbed by an expanding electric potential
• Y. Safarov -- On the comparison of the Dirichlet and Neumann counting functions
• O. Safronov -- Absolutely continuous spectrum of multi-dimensional Schrödinger operators with slowly decaying potentials
• R. Shterenberg -- On discrete spectrum of the perturbed periodic magnetic Schrödinger operator with degenerate lower edge of the spectrum
• T. A. Suslina -- Homogenization of periodic second order differential operators including first order terms
• T. Weidl -- Improved Berezin-Li-Yau inequalities with a remainder term
• D. R. Yafaev -- Spectral and scattering theory of fourth order differential operators