Random zero sets for Fock type spaces
Anna Kononova

TL;DR
This paper investigates the conditions under which randomly distributed points form zero sets in weighted Fock spaces, identifying critical densities and probabilistic criteria for these sets to be uniqueness sets.
Contribution
It introduces probabilistic methods to analyze zero sets in Fock spaces, establishing conditions and critical densities for random zero sets to occur almost surely.
Findings
Identifies conditions on sequences for zero sets in Fock spaces.
Determines the critical density of sequences relative to weights.
Establishes almost sure properties of random zero sets.
Abstract
Given a nondecreasing sequence such that we consider the sequence , where are independent random variables uniformly distributed on We discuss the conditions on the sequence under which is a zero set (a uniqness set) of a given weighted Fock space almost surely. The critical density of the sequence with respect to the weight is found.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Advanced Banach Space Theory
