On the Commutativity of the Berezin Transform
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866911199835193344 |
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| author | Borichev, Alexander Fantolini, Gérard Youssfi, El-Hassan |
| author_facet | Borichev, Alexander Fantolini, Gérard Youssfi, El-Hassan |
| contents | We consider the commutativity problem for the Berezin transform on weighted Fock spaces. Given a real number $m>0$, for every $α>0$ we denote by $B_α$ the Berezin transform associated to the measure $μ_{m}^α$ with density proportional to $e^{-α|z|^m}$ with respect to Lebesgue measure on the complex plane and normalized so that $μ_ϕ^α(\mathbb C)=1$. We show that the commutativity relation $B_αB_βf=B_βB_αf$ holds for all $f\in L^{\infty}(\mathbb C)$ and $α,β> 0$ if and only if $m=2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07887 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Commutativity of the Berezin Transform Borichev, Alexander Fantolini, Gérard Youssfi, El-Hassan Complex Variables 47B35, 30H20, 47B32 We consider the commutativity problem for the Berezin transform on weighted Fock spaces. Given a real number $m>0$, for every $α>0$ we denote by $B_α$ the Berezin transform associated to the measure $μ_{m}^α$ with density proportional to $e^{-α|z|^m}$ with respect to Lebesgue measure on the complex plane and normalized so that $μ_ϕ^α(\mathbb C)=1$. We show that the commutativity relation $B_αB_βf=B_βB_αf$ holds for all $f\in L^{\infty}(\mathbb C)$ and $α,β> 0$ if and only if $m=2$. |
| title | On the Commutativity of the Berezin Transform |
| topic | Complex Variables 47B35, 30H20, 47B32 |
| url | https://arxiv.org/abs/2510.07887 |