Frame bound, spectral gap and Plus space
Functional Analysis
2025-05-29 v1
Abstract
In this paper, we investigate the relationship between frame bounds and spectral gaps. By introducing the notion of \emph{essential minimum(maximal) spectral gap}, we provide a local characterization of Landau's theorem \cite{Lan67}. As an application, we resolve the spectrality additive measures of Lebesgue type, conclusively answering an open question on the spectrality of Plus spaces originally raised by Lai, Liu, Prince \cite{LLP21} and further studied by Ai, Lu, Zhou \cite{ALZ23} and Kolountzakis, Wu \cite{KW25}.
Cite
@article{arxiv.2505.22136,
title = {Frame bound, spectral gap and Plus space},
author = {Zheng-Yi Lu},
journal= {arXiv preprint arXiv:2505.22136},
year = {2025}
}