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arXiv · 2610.14599

Products of Berezin Transforms on Generalized Fock Spaces

Hao Tian
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Abstract

We study products $B_{α,m}^{(d)}B_{β,m}^{(d)}$ of Berezin transforms on generalized Fock spaces over $\mathbb C^d$. We establish a result for $m\neq2$: if $B_{α,m}^{(d)}B_{β,m}^{(d)}$ coincides with another such product, then the weight parameters of the second product must be $(α,β)$. As consequences, we characterize when two Berezin transforms commute and when the product of two Berezin transforms is again a Berezin transform.

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Hao Tian. 2026-10-10. Products of Berezin Transforms on Generalized Fock Spaces. https://arxiv.org/abs/2610.14599

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