A set with no Riesz basis of exponentials

2021/10/05 by Kozma, Gady, Nitzan, Shahaf, Olevskii, Alexander · 3 citations
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2110.02090

Abstract

We show that there exists a bounded subset of R such that no system of exponentials can be a Riesz basis for the corresponding Hilbert space. An additional result gives a lower bound for the Riesz constant of any putative Riesz basis of the two dimensional disk.

Cited by

• Exponential frames and Riesz sequences at the critical density
• Frame redundancy and Beurling density
• Exponential Riesz bases in non-Archimedean locally compact Abelian groups

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