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- W4320853718 abstract "We prove that the Beurling dimensions of the spectra for a class of Moran spectral measures are between $0$ and their upper entropy dimensions. Moreover, for such a Moran spectral measure $mu$, we show that the Beurling dimension for the spectra of $mu$ has the intermediate value property: let $t$ be any value between $0$ and the upper entropy dimension of $mu$, then there exists a spectrum whose Beurling dimension is $t.$ In particular, this result settles affirmatively a conjecture involving spectral Bernoulli convolution proposed by Fu, He and Wen in [J. Math. Pures Appl. 116 (2018), 105--131]. Furthermore, we prove that the set of the spectra whose Beurling dimensions are equal to any fixed value between $0$ and $ue mu$ has the cardinality of the continuum." @default.
- W4320853718 created "2023-02-16" @default.
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- W4320853718 date "2023-02-12" @default.
- W4320853718 modified "2023-09-29" @default.
- W4320853718 title "On the intermediate value property of spectra for a class of Moran spectral measures" @default.
- W4320853718 doi "https://doi.org/10.48550/arxiv.2302.05868" @default.
- W4320853718 hasPublicationYear "2023" @default.
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