Hypercyclicity of weighted shifts on weighted Bergman spaces

2025/03/20 by Bibhash Kumar Das, Das, Bibhash Kumar, Aneesh Mundayadan +1
Mathematics · #32K05 #37A99 #46E22 #47A16 #47B32 #47B37 #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.2503.16354

openalex publication_date 2025/03/20 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/30

Abstract

We study the continuity, and dynamical properties (hypercyclicity, periodic vectors, and chaos) for a weighted backward shift B_w on a weighted Bergman space A^p_ϕ based on the norm estimates of coefficient functionals on A^p_ϕ. Here, the weight function ϕ(z) is mostly radial, but our work will also involve a (non-radial) subharmonic weight. We provide a complete characterization of hypercyclic shifts B_w on A^p_ϕ when ϕ is an (integrable) radial weight. The coefficient multipliers obtained in this paper for certain weights are new.

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