Toeplitz operators with singular symbols in polyanalytic Bergman spaces on the half-plane
Book chapter, 2020
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.
Bergman space
Toeplitz operators
Author
Grigori Rozenblioum
Chalmers, Mathematical Sciences
Saint Petersburg State University - Spsu
N. Vasilevski
Centro de Investigacion y de Estudios Avanzados Centro de Investigacion y de Estudios Avanzados (CINVESTAV)
Operator Theory: Advances and Applications
02550156 (ISSN) 22964878 (eISSN)
Vol. 279 403-421978-3-030-44650-5 (ISBN)
Subject Categories (SSIF 2011)
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.1007/978-3-030-44651-2_23