TY  - BOOK
AU  - Vasilevski,Nikolai
ED  - SpringerLink (Online service)
TI  - Polyanalytic Type Function Spaces
T2  - Operator Theory: Advances and Applications,
SN  - 9783031761812
AV  - QA331.7 
PY  - 2024///
CY  - Cham
PB  - Springer Nature Switzerland, Imprint: Birkhäuser
KW  - Functions of complex variables
KW  - Operator theory
KW  - Several Complex Variables and Analytic Spaces
KW  - Operator Theory
KW  - Functions of a Complex Variable
N1  - 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
N2  - 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
UR  - https://doi.org/10.1007/978-3-031-76181-2
ER  -