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arXiv · 2201.10230

Toeplitz and related operators on polyanalytic Fock spaces

Raffael Hagger
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Abstract

We give a characterization of compact and Fredholm operators on polyanalytic Fock spaces in terms of limit operators. As an application we obtain a generalization of the Bauer-Isralowitz theorem using a matrix valued Berezin type transform. We then apply this theorem to Toeplitz and Hankel operators to obtain necessary and sufficient conditions for compactness. As it turns out, whether or not a Toeplitz or Hankel operator is compact does not depend on the polyanalytic order. For Hankel operators this even holds on the true polyanalytic Fock spaces.

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Raffael Hagger. 2022-01-25. Toeplitz and related operators on polyanalytic Fock spaces. https://arxiv.org/abs/2201.10230

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