2025/10/22 by Zi-Yun Chen, Ziyun Chen, Chen, Zi-Yun +5
Mathematics · #Advanced Operator Algebra Research #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods #math.CA #math.DS
paper · pdf · doi:10.48550/arxiv.2510.19187
openalex publication_date 2025/10/22 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28
It is well-known that the Beurling dimension of the spectra of certain singularly continuous spectral measures possesses an intermediate property. In this paper, we establish that for a class of self-affine spectral measures μ, both the Beurling dimension and Beurling density of their spectra attain full flexibility simultaneously. Specifically, for any t∈ (0,dimHw(\supp(μ))] and s∈ [0,∞), there exists a spectrum Λ:=Λt,s of μ satisfying dimBe(Λ)=t\quadand Dt+(Λ)=s where dimHw denotes the pseudo Hausdorff dimension, dimBe denotes the Beurling dimension and Dt+ denotes the t-Beurling density. These results provide new insights into the structure of the spectra for a singularly continuous spectral measure.