Toeplitz operators in polyanalytic bergman type spaces
Book chapter, 2019

We consider Toeplitz operators in Bergman and Fock type spaces of polyanalytic L2-functions on the disk or on the half-plane with respect to the Lebesgue measure (resp., on C with the plane Gaussian measure). The structure involving creation and annihilation operators, similar to the classical one present for the Landau Hamiltonian, enables us to reduce Toeplitz operators in true polyanalytic spaces to the ones in the usual Bergman type spaces, however with distributional symbols. This reduction leads to describing a number of properties of the operators in the title, which may differ from the properties of the usual Bergman-Toeplitz operators.

And phrases

Bergman spaces

Fock spaces

Toeplitz operators

Polyanalytic functions

Creation and annihilation


Grigori Rozenblioum

Saint Petersburg State University - Spsu

University of Gothenburg

Chalmers, Mathematical Sciences

N. Vasilevski

Centro de Investigacion y de Estudios Avanzados Centro de Investigacion y de Estudios Avanzados (CINVESTAV)

Contemporary Mathematics


Subject Categories

Algebra and Logic


Mathematical Analysis


Basic sciences



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