Functional Analysis and Geometry: Selim Grigorievich Krein Centennial

This is the first of two volumes dedicated to the centennial of the distinguished mathematician Selim Grigorievich Krein. The companion volume is Contemporary Mathematics, Volume 734. Krein was a major contributor to functional analysis, operator theory, partial differential equations, fluid dynamics, and other areas, and the author of several influential monographs in these areas. He was a prolific teacher, graduating 83 Ph.D. students. Krein also created and ran, for many years, the annual Voronezh Winter Mathematical Schools, which significantly influenced mathematical life in the former Soviet Union. The articles contained in this volume are written by prominent mathematicians, former students and colleagues of Selim Krein, as well as lecturers and participants of Voronezh Winter Schools. They are devoted to a variety of contemporary problems in functional analysis, operator theory, several complex variables, topological dynamics, and algebraic, convex, and integral geometry.

Table of Contents:
P. Kuchment and E. Semenov, Introduction T. Voronina (nee Krein), My father Selim Krein Y. M. Berezansky, Kyiv, Fall of 1943 through 1946. The rebirth of mathematics D. G. Ebin, Selim Gregorievich Krein in Stony Brook M. Agranovsky, On algebraically integrable bodies S. V. Astashkin, Rearrangement invariant spaces satisfying Dunford-Pettis criterion of weak compactness G. Belitskii and V. Rayskin, A new method of extension of local maps of Banach spaces. Applications and examples Y. M. Berezansky and A. A. Kalyuzhnyi, Two consequences of the associativity condition for a hypercomplex system with locally compact basis W. O. Bray and B. Rubin, Inversion formulas of integral geometry in real hyperbolic space V. M. Buchstaber and A. A. Glutsyuk, Total positivity, Grassmannian and modified Bessel functions C. Ciliberto, F. Flamini, and M. Zaidenberg, A remark on the intersection of plane curves A. T. Fomenko and V. V. Vedyushkina, Topological billiards, conservation laws and classification of trajectories L. Gatto and I. Scherbak, Hasse-Schmidt derivations and Cayley-Hamilton theorem for exterior algebras S. Gindikin, Complex analysis on the real sphere, or variations on a Maxwell's theme G. R. Goldstein, J. A. Goldstein, G. Metafune, and L. Negro, The weighted Laplace transform S. Kaliman, Surfaces with big automorphism groups P. Kuchment and S. Lvin, Some binomial formulas for non-commuting operators J. Leiterer, Similarity of holomorphic matrices on 1-dimensional Stein spaces V. Milman and L. Rotem, Weighted geometric means of convex bodies I. Z. Pesenson, Sobolev, Besov and Paley-Wiener vectors in Banach and Hilbert spaces G. Rozenblum and N. Vasilevski, Toeplitz operators in polyanalytic Bergman type spaces S. Samborski, Complete metric space of Riemann integrable functions and differential calculus in it.