Frame bound, spectral gap and Plus space

2025/05/28 by Z.-N. Lu, Lu, Zheng-Yi · 2 citations
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2505.22136

openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \citeLan67. 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 \citeLLP21 and further studied by Ai, Lu, Zhou \citeALZ23 and Kolountzakis, Wu \citeKW25.

Citations

• Spectrality of a measure consisting of two line segments
• Spectral properties of some unions of linear spaces
• The Fuglede conjecture for convex domains is true in all dimensions
• Spectra of Cantor measures
• Tiles with no spectra
• Tiles with no spectra
• Fuglede's conjecture is false in 5 and higher dimensions
• On Fourier frames
• Fuglede's conjecture for a union of two intervals
• How large are the spectral gaps?

Cited by

• Spectra for finite unions of line segments
• Non-spectrality of some piecewise smooth curves and unions of line segments

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