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Toeplitz operators with singular symbols in polyanalytic Bergman spaces on the half-plane. (English) Zbl 07244868

Bauer, Wolfram (ed.) et al., Operator algebras, Toeplitz operators and related topics. Selected papers based on the presentations at the international workshop, Boca del Rio, Veracruz, Mexico, November 13–19, 2018. In honor of Nikolai Vasilevskin on the occasion of his 70th birthday. Cham: Birkhäuser. Oper. Theory: Adv. Appl. 279, 403-421 (2020).
Summary: 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.
For the entire collection see [Zbl 1446.00025].

MSC:

47-XX Operator theory
46Lxx Selfadjoint operator algebras (\(C^*\)-algebras, von Neumann (\(W^*\)-) algebras, etc.)
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