Localization operators on Bergman and Fock spaces
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918369653948416 |
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| author | Ma, Pan Yan, Fugang Zheng, Dechao Zhu, Kehe |
| author_facet | Ma, Pan Yan, Fugang Zheng, Dechao Zhu, Kehe |
| contents | We introduce localization operators on weighted Bergman and Fock spaces and show that, under a natural scaling of symbols and window functions, localization operators on the weighted Bergman space $A_{βr^2}^2$ converge, in the weak sense, to localization operators on the Fock space $F_β^2$ as $r\to\infty$. From this we derive several applications, including one about sharp norm estimates for certain Toeplitz operators on Fock spaces, one about windowed Berezin transforms for weighted Bergman spaces, and another about Szegö-type theorems for localization operators on weighted Bergman spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04051 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Localization operators on Bergman and Fock spaces Ma, Pan Yan, Fugang Zheng, Dechao Zhu, Kehe Functional Analysis Complex Variables We introduce localization operators on weighted Bergman and Fock spaces and show that, under a natural scaling of symbols and window functions, localization operators on the weighted Bergman space $A_{βr^2}^2$ converge, in the weak sense, to localization operators on the Fock space $F_β^2$ as $r\to\infty$. From this we derive several applications, including one about sharp norm estimates for certain Toeplitz operators on Fock spaces, one about windowed Berezin transforms for weighted Bergman spaces, and another about Szegö-type theorems for localization operators on weighted Bergman spaces. |
| title | Localization operators on Bergman and Fock spaces |
| topic | Functional Analysis Complex Variables |
| url | https://arxiv.org/abs/2603.04051 |