LEADER 03248nam 22005055 450 001 9910917189403321 005 20251113201852.0 010 $a3-031-73430-0 024 7 $a10.1007/978-3-031-73430-4 035 $a(CKB)36959113300041 035 $a(MiAaPQ)EBC31824069 035 $a(Au-PeEL)EBL31824069 035 $a(DE-He213)978-3-031-73430-4 035 $a(OCoLC)1478698017 035 $a(EXLCZ)9936959113300041 100 $a20241210d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuaternionic Hilbert Spaces and Slice Hyperholomorphic Functions /$fby Daniel Alpay, Fabrizio Colombo, Irene Sabadini 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2024. 215 $a1 online resource (352 pages) 225 1 $aOperator Theory: Advances and Applications,$x2296-4878 ;$v304 311 08$a3-031-73429-7 327 $a- Part I Quaternionic functional analysis and related topics -- Functions of a Quaternionic Variable -- Quaternionic Banach and Hilbert Spaces -- Quaternionic Linear Operators on a Hilbert Space -- Reproducing Kernel Hilbert Spaces -- Part II Spaces of Slice Hyperholomorphic Functions -- Slice Hyperholomorphic Hardy Spaces -- de Branges Spaces -- Slice Hyperholomorphic Bergman Spaces -- Slice Hyperholomorphic Bloch, Besov and Dirichlet Spaces -- Slice Hyperholomorphic Fock Space -- Wiener Algebras -- Part III Various Extensions -- Slice Polyanalytic Functions -- Several Quaternionic Variables -- Function Spaces and Spectral Theories. 330 $aThe purpose of the present book is to develop the counterparts of Banach and Hilbert spaces in the setting of slice hyperholomorphic functions. Banach and Hilbert spaces of analytic functions, in one or several complex variables, play an important role in analysis and related fields. Besides their intrinsic interest, such spaces have numerous applications. The book is divided into three parts. In the first part, some foundational material on quaternionic functions and functional analysis are introduced. The second part is the core of the book and contains various types of functions spaces ranging from the Hardy spaces, also in the fractional case, to the Fock space extended to the case of quaternions. The third and final part present some further generalization. Researchers in functional analysis and hypercomplex analysis will find this book a key contribution to their field, but also researchers in mathematical physics, especially in quantum mechanics, will benefit from the insights presented. 410 0$aOperator Theory: Advances and Applications,$x2296-4878 ;$v304 606 $aOperator theory 606 $aOperator Theory 615 0$aOperator theory. 615 14$aOperator Theory. 676 $a515.724 700 $aAlpay$b Daniel$054298 701 $aColombo$b Fabrizio$0511074 701 $aSabadini$b Irene$0511075 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910917189403321 996 $aQuaternionic Hilbert Spaces and Slice Hyperholomorphic Functions$94303189 997 $aUNINA