This paper demonstrates harmonic fixed points of the Berezin transform in Fock-type spaces, showing implications for polynomial behavior.
We study the fixed points of the Berezin transform on the Fock-type spaces Fₘ² with the weight e-|z|ᵐ, m > 0. It is known that the Berezin transform is well-defined on the polynomials in z and z̄. 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 ∈ (0, ∞). We also show that, in some particular cases, the fixed point polynomials are harmonic for all $m.$
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Asghari et al. (2025) studied this question.
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