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 Algebras, Toeplitz Operators and Related Topics, Bauer W., Duduchava R., Grudsky S., Kaashoek M. (eds), (Operator Theory: Advances and Applications, vol 279)
403-421
Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.1007/978-3-030-44651-2_23