03091nam a22005295i 4500 978-3-031-76181-2 DE-He213 20251030114912.0 cr nn 008mamaa 241231s2024 sz | s |||| 0|eng d 9783031761812 978-3-031-76181-2 10.1007/978-3-031-76181-2 doi QA331.7 PBKD bicssc MAT034000 bisacsh PBKD thema Vasilevski, Nikolai. author. aut http://id.loc.gov/vocabulary/relators/aut 89955 Polyanalytic Type Function Spaces [electronic resource] / by Nikolai Vasilevski. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2024. XXX, 174 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Operator Theory: Advances and Applications, 2296-4878 ; 305 Foreword -- 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 Π 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. This 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. Functions of complex variables. 72222 Operator theory. Several Complex Variables and Analytic Spaces. 72225 Operator Theory. Functions of a Complex Variable. 72224 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031761805 Printed edition: 9783031761829 Printed edition: 9783031761836 Operator Theory: Advances and Applications, 2296-4878 ; 305 74617 https://doi.org/10.1007/978-3-031-76181-2 ZDB-2-SMA ZDB-2-SXMS 66232 66232