Self-similar sets and measures on the line

2021/09/22 by Péter P. Varjú, Varjú, Péter P. · 1 citation
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2109.10629

openalex publication_date 2021/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the problem of determining the dimension of self-similar sets and measures on R. We focus on the developments of the last four years. At the end of the paper, we survey recent results about other aspects of self-similar measures including their Fourier decay and absolute continuity.

Citations

• Absolute Continuity of Self Similar Measures

Cited by

• Entropy rates in the dimension theory of self-similar measures

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