LEADER 02565nam 22004575a 450 001 9910151929303321 005 20110225234510.0 010 $a3-03719-580-0 024 70$a10.4171/080 035 $a(CKB)3710000000953865 035 $a(CH-001817-3)126-110225 035 $a(PPN)178155888 035 $a(EXLCZ)993710000000953865 100 $a20110225j20110225 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLectures on Gaussian Integral Operators and Classical Groups$b[electronic resource] /$fYurii A. Neretin 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2011 215 $a1 online resource (571 pages) 225 0 $aEMS Series of Lectures in Mathematics (ELM) ;$x2523-5176 330 $aThis 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. 606 $aGroups & group theory$2bicssc 606 $aTopological groups, Lie groups$2msc 606 $aSeveral complex variables and analytic spaces$2msc 606 $aOperator theory$2msc 606 $aDifferential geometry$2msc 615 07$aGroups & group theory 615 07$aTopological groups, Lie groups 615 07$aSeveral complex variables and analytic spaces 615 07$aOperator theory 615 07$aDifferential geometry 686 $a22-xx$a32-xx$a47-xx$a53-xx$2msc 700 $aNeretin$b Yurii A.$057370 801 0$bch0018173 906 $aBOOK 912 $a9910151929303321 996 $aLectures on Gaussian Integral Operators and Classical Groups$92565443 997 $aUNINA