LEADER 02975nam 22005775 450 001 9910919811603321 005 20251113182403.0 010 $a9783031761812 010 $a3031761812 024 7 $a10.1007/978-3-031-76181-2 035 $a(CKB)37115970800041 035 $a(MiAaPQ)EBC31868116 035 $a(Au-PeEL)EBL31868116 035 $a(DE-He213)978-3-031-76181-2 035 $a(EXLCZ)9937115970800041 100 $a20241231d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aPolyanalytic Type Function Spaces /$fby Nikolai Vasilevski 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (199 pages) 225 1 $aOperator Theory: Advances and Applications,$x2296-4878 ;$v305 311 08$a9783031761805 311 08$a3031761804 320 $aIncludes bibliographical references and index. 327 $aForeword -- Preface -- Introduction -- I Spaces of polyanalytic type in one complex variable -- 1 Extended Fock-space construction approach -- 2 Complex plane C case -- 3 Unit disk D case -- 4 Upper half-plane ? case -- 5 Basis oriented approach -- 6 Approach based on pure isometries -- II Spaces of polyanalytic type in several complex variables -- 7 Multi-operator extended Fock-space construction -- 8 The Cn case -- 9 The unit ball Bn case -- 10 Hilbert spaces with generalized Gaussian measure on C2 -- 11 The Siegel domain case -- Bibliography -- Index. 330 $aThis book is about function spaces aspects of polyanalytic functions, a topic that has gained a lot of attention in the past decades. This book fills a gap in literature and is written by a leading researcher in the field. Rather than studying polyanalytic functions from a complex analysis point of view, it considers the (Lie)-algebraic part of the theory. Several generalizations are offered. The presented theory has many applications, including to quantum physics. An extensive introduction to the topic is provided, making the book accessible to specialists and newcomers alike. 410 0$aOperator Theory: Advances and Applications,$x2296-4878 ;$v305 606 $aFunctions of complex variables 606 $aOperator theory 606 $aSeveral Complex Variables and Analytic Spaces 606 $aOperator Theory 606 $aFunctions of a Complex Variable 615 0$aFunctions of complex variables. 615 0$aOperator theory. 615 14$aSeveral Complex Variables and Analytic Spaces. 615 24$aOperator Theory. 615 24$aFunctions of a Complex Variable. 676 $a516.3 700 $aVasilevski$b Nikolai$0504977 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910919811603321 996 $aPolyanalytic Type Function Spaces$94306415 997 $aUNINA