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