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| Format: | Preprint |
| Published: |
2025
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| Online Access: | https://arxiv.org/abs/2505.22136 |
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| _version_ | 1866910972765011968 |
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| author | Lu, Zheng-Yi |
| author_facet | Lu, Zheng-Yi |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_22136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Frame bound, spectral gap and Plus space Lu, Zheng-Yi Functional Analysis 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}. |
| title | Frame bound, spectral gap and Plus space |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2505.22136 |