Polyanalytic Toeplitz Operators: Isomorphisms, Symbolic Calculus and Approximation of Weyl Operators
Peer reviewed, Journal article
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Date
2021Metadata
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- Institutt for matematiske fag [2532]
- Publikasjoner fra CRIStin - NTNU [38672]
Original version
https://doi.org/10.1007/s00041-021-09843-0Abstract
We discuss an extension of Toeplitz quantization based on polyanalytic functions. We derive isomorphism theorem for polyanalytic Toeplitz operators between weighted Sobolev-Fock spaces of polyanalytic functions, which are images of modulation spaces under polyanalytic Bargmann transforms. This generalizes well-known results from the analytic setting. Finally, we derive an asymptotic symbol calculus and present an asymptotic expansion of complex Weyl operators in terms of polyanalytic Toeplitz operators.