02975nam 22005775 450 991091981160332120251113182403.09783031761812303176181210.1007/978-3-031-76181-2(CKB)37115970800041(MiAaPQ)EBC31868116(Au-PeEL)EBL31868116(DE-He213)978-3-031-76181-2(EXLCZ)993711597080004120241231d2024 u| 0engur|||||||||||txtrdacontentcrdamediacrrdacarrierPolyanalytic Type Function Spaces /by Nikolai Vasilevski1st ed. 2024.Cham :Springer Nature Switzerland :Imprint: Birkhäuser,2024.1 online resource (199 pages)Operator Theory: Advances and Applications,2296-4878 ;3059783031761805 3031761804 Includes bibliographical references and index.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.Operator Theory: Advances and Applications,2296-4878 ;305Functions of complex variablesOperator theorySeveral Complex Variables and Analytic SpacesOperator TheoryFunctions of a Complex VariableFunctions of complex variables.Operator theory.Several Complex Variables and Analytic Spaces.Operator Theory.Functions of a Complex Variable.516.3Vasilevski Nikolai504977MiAaPQMiAaPQMiAaPQBOOK9910919811603321Polyanalytic Type Function Spaces4306415UNINA