This first of a two-volume collection is a celebration of the scientific heritage of F. A. Berezin (1931-1980). 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 three-body 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 Berezin-Lieb inequality
• V. F. Molchanov -- Quantization on para-Hermitian 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