IDA and Hankel operators on Fock spaces
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866914830146863104 |
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| author | Hu, Zhangjian Virtanen, Jani A. |
| author_facet | Hu, Zhangjian Virtanen, Jani A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2111_04821 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | IDA and Hankel operators on Fock spaces Hu, Zhangjian Virtanen, Jani A. Functional Analysis Mathematical Physics Complex Variables 47B35, 32A25, 32A37, 81S10 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. |
| title | IDA and Hankel operators on Fock spaces |
| topic | Functional Analysis Mathematical Physics Complex Variables 47B35, 32A25, 32A37, 81S10 |
| url | https://arxiv.org/abs/2111.04821 |