关于一类Moran谱测度的谱的中值性质

IF 2.6 2区数学 Q1 MATHEMATICS, APPLIED

Applied and Computational Harmonic Analysis Pub Date : 2023-11-08 DOI:10.1016/j.acha.2023.101606

Jinjun Li, Zhiyi Wu

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引用次数: 3

摘要

我们证明了一类Moran谱测度的谱的Beurling维数在0及其上熵维数。此外，对于这样的Moran谱测度μ，我们证明了μ的谱的Beurling维数具有中间值性质：设t为0中的任何值和μ的上熵维数，则存在Beurling维为t的谱。特别地，这一结果肯定地解决了[J.Math.Pures Appl.116（2018），105–131]中涉及谱伯努利卷积的猜想。此外，我们证明了Beurling维数等于0和dim‾eμ中任何固定值的谱集具有连续体的基数。

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On the intermediate value property of spectra for a class of Moran spectral measures

We prove that the Beurling dimensions of the spectra for a class of Moran spectral measures are in 0 and their upper entropy dimensions. Moreover, for such a Moran spectral measure μ, we show that the Beurling dimension for the spectra of μ has the intermediate value property: let t be any value in 0 and the upper entropy dimension of μ, then there exists a spectrum whose Beurling dimension is t. In particular, this result settles affirmatively a conjecture involving spectral Bernoulli convolution in Fu et al. (2018) [20]. Furthermore, we prove that the set of the spectra whose Beurling dimensions are equal to any fixed value in 0 and ${\overline{\dim}}_{e} μ$ has the cardinality of the continuum.

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来源期刊

Applied and Computational Harmonic Analysis 物理-物理：数学物理

CiteScore

5.40

自引率

4.00%

发文量

审稿时长

22.9 weeks

期刊介绍： Applied and Computational Harmonic Analysis (ACHA) is an interdisciplinary journal that publishes high-quality papers in all areas of mathematical sciences related to the applied and computational aspects of harmonic analysis, with special emphasis on innovative theoretical development, methods, and algorithms, for information processing, manipulation, understanding, and so forth. The objectives of the journal are to chronicle the important publications in the rapidly growing field of data representation and analysis, to stimulate research in relevant interdisciplinary areas, and to provide a common link among mathematical, physical, and life scientists, as well as engineers.