Toeplitz Operators with Singular Symbols in Polyanalytic Bergman Spaces on the Half-Plane

Nikolai Vasilevski,Grigori Rozenblum

doi:10.1007/978-3-030-44651-2_23

Toeplitz Operators with Singular Symbols in Polyanalytic Bergman Spaces on the Half-Plane

Nikolai Vasilevski, Grigori Rozenblum

Open Access

https://doi.org/10.1007/978-3-030-44651-2_23

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Publication Date: Jan 1, 2020

Citations: 1

Affiliation: Center for Research and Advanced Studies of the National Polytechnic Institute, Chalmers University of Technology, University of Gothenburg, St Petersburg University

#Singular Symbols #Toeplitz Operators + Show 8 more

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Abstract

Using the approach based on sesquilinear forms, we introduce Toeplitz operators in the analytic Bergman space on the upper half-plane with strongly singular symbols, derivatives of measures. Conditions for boundedness and compactness of such operators are found. A procedure of reduction of Toeplitz operators in Bergman spaces of polyanalytic functions to operators with singular symbols in the analytic Bergman space by means of the creation-annihilation structure is elaborated, which leads to the description of the properties of the former operators.

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