Polyanalytic Type Function Spaces

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.

• 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.