Fixed points of the Berezin transform on Fock-type spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911330819112960 |
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| author | Asghari, Ghazaleh Cuckovic, Zeljko Sahutoglu, Sonmez |
| author_facet | Asghari, Ghazaleh Cuckovic, Zeljko Sahutoglu, Sonmez |
| contents | We study the fixed points of the Berezin transform on the Fock-type spaces $F_m^2$ with the weight $e^{-|z|^m}, m > 0.$ It is known that the Berezin transform is well-defined on the polynomials in $z$ and $\overline{z}$. In this paper we focus on the polynomial fixed points and we show that these polynomials must be harmonic, except possibly for countably many $m \in (0, \infty).$ We also show that, in some particular cases, the fixed point polynomials are harmonic for all $m.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_13115 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed points of the Berezin transform on Fock-type spaces Asghari, Ghazaleh Cuckovic, Zeljko Sahutoglu, Sonmez Complex Variables Functional Analysis We study the fixed points of the Berezin transform on the Fock-type spaces $F_m^2$ with the weight $e^{-|z|^m}, m > 0.$ It is known that the Berezin transform is well-defined on the polynomials in $z$ and $\overline{z}$. In this paper we focus on the polynomial fixed points and we show that these polynomials must be harmonic, except possibly for countably many $m \in (0, \infty).$ We also show that, in some particular cases, the fixed point polynomials are harmonic for all $m.$ |
| title | Fixed points of the Berezin transform on Fock-type spaces |
| topic | Complex Variables Functional Analysis |
| url | https://arxiv.org/abs/2508.13115 |