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arXiv · 2207.02723

Random zero sets for Fock type spaces

Anna Kononova
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Abstract

Given a nondecreasing sequence $\Lambda=\{\lambda_n>0\}$ such that $\displaystyle\lim_{n\to\infty} \lambda_n=\infty,$ we consider the sequence $\mathcal N_\Lambda:=\left\{\lambda_ne^{i\theta_n},n\in\,\mathbb N\right\}$, where $\theta_n$ are independent random variables uniformly distributed on $[0,2\pi].$ We discuss the conditions on the sequence $\Lambda$ under which $\mathcal N_\Lambda$ is a zero set (a uniqness set) of a given weighted Fock space almost surely. The critical density of the sequence $\Lambda$ with respect to the weight is found.

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Anna Kononova. 2022-07-06. Random zero sets for Fock type spaces. https://arxiv.org/abs/2207.02723

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