American Mathematical Society TranslationsSeries 2 Advances in the Mathematical Sciences 1996; 236 pp; hardcover Volume: 175 ISBN10: 082180426X ISBN13: 9780821804261 List Price: US$120 Member Price: US$96 Order Code: TRANS2/175
 This first of a twovolume collection is a celebration of the scientific heritage of F. A. Berezin (19311980). Before his untimely death, Berezin had an important influence on physics and mathematics, discovering new ideas in mathematical physics, representation theory, analysis, geometry, and other areas of mathematics. His crowning achievements were the introduction of a new notion of deformation quantization, and Grassmannian analysis ("supermathematics"). Collected here are papers by his many of his colleagues and others who worked in related areas, representing a wide spectrum of topics in mathematical physics and allied areas of mathematics. In particular, the papers discuss quantization, invariant integration, spectral theory, and representation theory. Readership Graduate students and research mathematicians interested in group representation theory, supermathematics, and spectral analysis. Table of Contents  R. A. Minlos  Felix Alexandrovich Berezin (a brief scientific biography)
 V. M. Buchstaber and A. M. Perelomov  On the functional equation related to the quantum threebody problem
 L. D. Faddeev and P. N. Pyatov  The differential calculus on quantum linear groups
 S. Gindikin  The Penrose transform on flag domains in \(\mathcal F(\mathbb CP^2)\)
 P. Grozman and D. Leites  Defining relations associated with principal \(\mathfrak {sl}(2)\)subalgebras
 A. Laptev and Yu. Safarov  A generalization of the BerezinLieb inequality
 V. F. Molchanov  Quantization on paraHermitian symmetric spaces
 Yu. A. Neretin  Integral operators with Gaussian kernels and symmetries of canonical commutation relations
 G. Olshanski and A. Vershik  Ergodic unitarily invariant measures on the space of infinite Hermitian matrices
 V. P. Palamodov  Cogitations on Berezin's integral
 M. A. Shubin  Remarks on the topology of the Hilbert Grassmannian
 I. M. Sigal  Asymptotic completeness
 D. P. Zhelobenko  Constructive modules and the reductivity problem in the category \(\mathcal O\)
 Alik Berezin in the recollections of friends
