Sampling constants in generalized Fock spaces

TL;DR

This paper establishes a Logvinenko-Sereda type theorem for generalized doubling Fock spaces, providing explicit polynomial bounds on sampling constants based on the density of dominating sets.

Contribution

It extends techniques from Bergman spaces to generalized Fock spaces, offering precise polynomial estimates for sampling constants in terms of set density.

Findings

Polynomial dependence of sampling constants on density parameter b3

Adaptation of Remez-type inequality for doubling measures

New covering lemma for generalized Fock spaces

Abstract

We prove several results related to a Logvinenko-Sereda type theorem on dominating sets for generalized doubling Fock spaces. In particular, we give a precise polynomial dependence of the sampling constant on the relative density parameter $\gamma$ of the dominating set. Our method is an adaptation of that used in \cite{HKO} for the Bergman spaces and is based on a Remez-type inequality and a covering lemma related to doubling measures.