This volume is devoted to the 25-year-old Voronezh Winter Mathematical School and to the scientific work of its founder, Selim Krein. The Voronezh Winter Mathematical School was a unique annual event in the scientific life of the former Soviet Union. Over the years it attracted thousands of mathematicians, from undergraduates to world-renowned experts, and played a major role in spreading information about cutting edge results of mathematical research, triggering cooperation and educating new generations of mathematicians. The articles in this book, written by prominent mathematicians and former lecturers and participants of the school, cover a wide range of subjects in analysis and geometry, including global analysis, harmonic analysis, function theory, operator theory, spectral theory, dynamical systems, mathematical physics, homogenization, algebraic geometry, differential geometry, and geometric analysis.
Fredholm property of functional equations with affine transformations of argument by G. Belitskii and V. Tkachenko Construction of generalized translation operators from the system of Appell characters by Y. M. Berezansky Witten deformation of the analytic torsion and the Reidemeister torsion by D. Burghelea, L. Friedlander, and T. Kappeler Formal operator power series and the noncommutative Taylor formula by Y. L. Daletskii Plane curves with a big fundamental group of the complement by G. Dethloff, S. Orevkov, and M. Zaidenberg Solution of the linearized inverse conductivity problem in a half space via integral geometry by B. Fridman, P. Kuchment, D. Ma, and V. G. Papanicolaou Almost periodic factorization: Applicability of the division algorithm by M. Gelfand and I. M. Spitkovsky Liouville and Caratheodory coverings in Riemannian and complex geometry by V. Ya. Lin and M. Zaidenberg How big is the set of infinitely renormalizable quadratics? by M. Lyubich Linear operators in one-dimensional extensions of Banach spaces by Y. Lyubich Random rearrangements and operators by S. Montgomery-Smith and E. Semenov On reiteration theorems by V. I. Ovchinnikov Statistical homogenization theorem for multivalued monotone elliptic operators by A. Pankov Reconstruction of Paley-Wiener functions on the Heisenberg group by I. Pesenson De Rham theorem for extended $L^2$-cohomology by M. Shubin On the discrete spectrum of a class of problems involving the Neumann Laplacian in unbounded domains by M. Solomyak Szego-type extremal problems by N. Zobin.