Polyanalytic Type Function Spaces

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.

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 ? 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.

Nikolai Vasilevski was a professor at the Department of Mathematics of CINVESTAV del I.P.N., Mexico City, Mexico. He moved there in 1992 from Odessa, Ukraine, where he worked at the Department of Mathematics of Odessa State University.

He is the author of the monograph “Commutative Algebras of Toeplitz Operators on the Bergman Space” appeared at Birkhäuser in 2008.