Beurling dimension and a class of Moran measures

Authors：Wang, Cong; Zhang, Min-Min^*

Source：Chaos, Solitons and Fractals, 2023, 166: 112926.

DOI：10.1016/j.chaos.2022.112926

• Beurling dimension
• Moran measure
• Spectrum
• Hausdorff dimension

In this paper, we will study the Beurling dimension of spectra for Moran measures defined by infinite convolution of discrete measures @@@ [GRAPHICS] @@@ We obtain the upper and lower bounds of the dimension. More precisely, the upper bound is the Hausdorff dimension of the compact support of mu(b,D,{nj}) and the lower bound is 0. The bounds are attained in special cases and some examples are given to explain our theory.