2019/07/16 by Grigori Rozenblum, Rozenblum, Grigori, Nikolai Vasilevski +1
Mathematics · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1907.06878
openalex publication_date 2019/07/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using the approach based on sesquilinear forms, we introduce Toeplitz operator 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