IDA and Hankel operators on Fock spaces

Hu, Z. and Virtanen, J. A. (2023) IDA and Hankel operators on Fock spaces. Analysis & PDE, 16 (9). pp. 2041-2077. ISSN 1948-206X doi: 10.2140/apde.2023.16.2041

Abstract/Summary

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 Hf is compact if and only if H¯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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/104927
Identification Number/DOI	10.2140/apde.2023.16.2041
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Mathematical Sciences Publishers
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