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Sampling constants in generalized Fock spaces (2103.11653v3)
Published 22 Mar 2021 in math.CA, math.CV, and math.FA
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.
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