2023/02/12 by Jinjun Li, Li, Jinjun, Zhiyi Wu +1 · 1 citation
Mathematics · #Analytic and geometric function theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2302.05868
openalex publication_date 2023/02/12 · openalex created_date 2023/02/16 · openalex updated_date 2026/07/28
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 μ, we show that the Beurling dimension for the spectra of μ has the intermediate value property: let t be any value between 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 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 μ has the cardinality of the continuum.