02565nam 22004575a 450 991015192930332120110225234510.03-03719-580-010.4171/080(CKB)3710000000953865(CH-001817-3)126-110225(PPN)178155888(EXLCZ)99371000000095386520110225j20110225 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierLectures on Gaussian Integral Operators and Classical Groups[electronic resource] /Yurii A. NeretinZuerich, Switzerland European Mathematical Society Publishing House20111 online resource (571 pages)EMS Series of Lectures in Mathematics (ELM) ;2523-5176This book is an elementary self-contained introduction to some constructions of representation theory and related topics of differential geometry and analysis. Topics covered include the theory of various Fourier-like integral operators as Segal-Bargmann transforms, Gaussian integral operators in $L^2$ and in the Fock space, integral operators with theta-kernels, the geometry of real and $p$-adic classical groups and symmetric spaces. The heart of the book is the Weil representation of the symplectic group (real and complex realizations, relations with theta-functions and modular forms, $p$-adic and adelic constructions) and representations in Hilbert spaces of holomorphic functions of several complex variables. The book is addressed to graduate students and researchers in representation theory, differential geometry, and operator theory. The reader is supposed to be familiar with standard university courses in linear algebra, functional analysis, and complex analysis.Groups & group theorybicsscTopological groups, Lie groupsmscSeveral complex variables and analytic spacesmscOperator theorymscDifferential geometrymscGroups & group theoryTopological groups, Lie groupsSeveral complex variables and analytic spacesOperator theoryDifferential geometry22-xx32-xx47-xx53-xxmscNeretin Yurii A.57370ch0018173BOOK9910151929303321Lectures on Gaussian Integral Operators and Classical Groups2565443UNINA