On the projections of the multifractal Hewitt-Stromberg dimension functions

2019/11/20 by Bilel Selmi, Selmi, Bilel
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #28A20 #28A78 #28A80 #Complex Systems and Time Series Analysis #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1911.09643

openalex publication_date 2019/11/20 · openalex created_date 2019/12/05 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to study the behavior of the multifractal Hewitt-Stromberg dimension functions under projections in Euclidean space. As an application, we study the multifractal analysis of the projections of a measure. In particular, we obtain general results for the multifractal analysis of the orthogonal projections on m-dimensional linear subspaces of a measure μ satisfying the multifractal formalism which is based on the Hewitt-Stromberg measures.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.
• Strong Marstrand theorems and dimensions of sets formed by subsets of\n hyperplanes
• A capacity approach to box and packing dimensions of projections of sets\n and exceptional directions

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