IDA and Hankel operators on Fock spaces

We introduce a new space IDA of locally integrable functions whose integral distance to holomorphic functions is finite, and use it to completely characterize boundedness and compactness of Hankel operators on weighted Fock spaces. As an application, for bounded symbols, we show that the Hankel oper...

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Veröffentlicht in:	arXiv.org 2022-04
Hauptverfasser:	Hu, Zhangjian, Virtanen, Jani A
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Sprache:	eng
Schlagworte:	Analytic functions Mathematical functions Mathematics - Complex Variables Mathematics - Functional Analysis Mathematics - Mathematical Physics Operators (mathematics) Physics - Mathematical Physics
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description	We introduce a new space IDA of locally integrable functions whose integral distance to holomorphic functions is finite, and use it to completely characterize boundedness and compactness of Hankel operators on weighted Fock spaces. As an application, for bounded symbols, we show that the Hankel operator $H_f$ is compact if and only if $H_{\bar f}$ is compact, which complements the classical compactness result of Berger and Coburn. Motivated by recent work of Bauer, Coburn, and Hagger, we also apply our results to the Berezin-Toeplitz quantization.
doi_str_mv	10.48550/arxiv.2111.04821
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subjects	Analytic functions Mathematical functions Mathematics - Complex Variables Mathematics - Functional Analysis Mathematics - Mathematical Physics Operators (mathematics) Physics - Mathematical Physics
title	IDA and Hankel operators on Fock spaces
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