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arXiv · 2503.16354

Hypercyclicity of weighted shifts on weighted Bergman spaces

Bibhash Kumar Das·Aneesh Mundayadan
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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 $A^p_{\phi}$ based on the norm estimates of coefficient functionals on $A^p_{\phi}$. Here, the weight function $\phi(z)$ 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 $A^p_{\phi}$ when $\phi$ is an (integrable) radial weight. The coefficient multipliers obtained in this paper for certain weights are new.

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Bibhash Kumar Das, Aneesh Mundayadan. 2025-03-20. Hypercyclicity of weighted shifts on weighted Bergman spaces. https://arxiv.org/abs/2503.16354

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