Frame bound, spectral gap and Plus space
Abstract
In this paper, we investigate the relationship between frame bounds and spectral gaps. By introducing the notion of essential minimum(maximal) spectral gap, we provide a local characterization of Landau's theorem 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 LLP21 and further studied by Ai, Lu, Zhou ALZ23 and Kolountzakis, Wu KW25.
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