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arXiv · 1905.07741

Polyanalytic Toeplitz operators: isomorphisms, symbolic calculus and approximation of Weyl operators

Johannes Keller·Franz Luef
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Abstract

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.

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Johannes Keller, Franz Luef. 2019-05-19. Polyanalytic Toeplitz operators: isomorphisms, symbolic calculus and approximation of Weyl operators. https://arxiv.org/abs/1905.07741

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