Fixed points of the Berezin transform of polyanlytic Fock spaces

2019/03/13 by Irène Casseli, Casseli, Irène
Mathematics · #30G20 #30G30 #44A15 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1903.05364

openalex publication_date 2019/03/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the fixed points of the Berezin transform in polyanalytic Fock spaces of ℂ. We show that an L^p function, p∈[1,+∞], with respect to the Lebesgue measure is invariant under this transformation if and only if it is harmonic. From this we deduce that the only bounded fixed points of the Berezin transform of polyanalytic Fock spaces are constant functions.

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