Polyanalytic Toeplitz Operators: Isomorphisms, Symbolic Calculus and Approximation of Weyl Operators
Peer reviewed, Journal article
Published version
Åpne
Permanent lenke
https://hdl.handle.net/11250/2755848Utgivelsesdato
2021Metadata
Vis full innførselSamlinger
- Institutt for matematiske fag [2350]
- Publikasjoner fra CRIStin - NTNU [37186]
Originalversjon
https://doi.org/10.1007/s00041-021-09843-0Sammendrag
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.