Fractal uncertainty principle for discrete Cantor sets with random alphabets

2021/07/17 by Suresh Eswarathasan, Eswarathasan, Suresh, Xiaolong Han +1
Computer Science · Mathematics · #42A38 #60E15 #60G42 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Probability (math.PR) #Spectral Theory (math.SP) #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2107.08276

openalex publication_date 2021/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the fractal uncertainty principle (FUP) for discrete Cantor sets, which are determined by an alphabet from a base of digits. Consider the base of M digits and the alphabets of cardinality A such that all the corresponding Cantor sets have a fixed dimension 0

Citations

• Additive energy of regular measures in one and higher dimensions, and the fractal uncertainty principle

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