03698nam a22005175i 4500 978-3-031-73430-4 DE-He213 20251030114610.0 cr nn 008mamaa 241210s2024 sz | s |||| 0|eng d 9783031734304 978-3-031-73430-4 10.1007/978-3-031-73430-4 doi QA329-329.9 PBKF bicssc MAT037000 bisacsh PBKF thema Alpay, Daniel. author. aut http://id.loc.gov/vocabulary/relators/aut 76556 Quaternionic Hilbert Spaces and Slice Hyperholomorphic Functions [electronic resource] / by Daniel Alpay, Fabrizio Colombo, Irene Sabadini. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XI, 348 p. 29 illus., 1 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Operator Theory: Advances and Applications, 2296-4878 ; 304 - 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. The 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. Operator theory. Operator Theory. Colombo, Fabrizio. author. aut http://id.loc.gov/vocabulary/relators/aut 29137 Sabadini, Irene. author. aut http://id.loc.gov/vocabulary/relators/aut 29138 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031734298 Printed edition: 9783031734311 Printed edition: 9783031734328 Operator Theory: Advances and Applications, 2296-4878 ; 304 74617 https://doi.org/10.1007/978-3-031-73430-4 ZDB-2-SMA ZDB-2-SXMS 65601 65601