Beurling dimension and self-similar measures
type: Item
instance of: scholarly article
title: Beurling dimension and self-similar measures
zbMATH Open document ID: 1384.28015
author: Xing-Gang He
author: Qing-can Kang
author: Min-wei Tang
author: Zhi-Yi Wu
published in: Journal of Functional Analysis
publication date: 2018-02-28T00:00:00Z
review text: The authors prove that the following conjecture is true for Bessel sets of a self-similar measure \(\mu\) on \(\mathbb{R}^d\) which satisfies the open set condition and has different contraction ratios and different probability weights: Conjecture. Let \(\mu\) be a Borel probability measure with compact support \(T\subset\mathbb{R}^d\). If \(\mu\) is a frame spectral measure with frame spectrum \(\Lambda\) then \[ \dim_B \Lambda \leq \dim_H T, \] where \(\dim_B\) denotes the Beurling and \(\dim_H\) the Hausdorff dimension. Several examples are given to illustrate the result.
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 6845288
zbMATH Keywords: Beurling dimension
zbMATH Keywords: Fourier-Bessel measure
zbMATH Keywords: Fourier frame
zbMATH Keywords: Hausdorff dimension
zbMATH Keywords: iterated function system (IFS)
reviewed by: Peter Massopust
MaRDI profile type: Publication
full work available at URL: j.jfa.2017.08.011
OpenAlex ID: W2745595434
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DOI: 10.1016/J.JFA.2017.08.011
description: scientific article; zbMATH DE number 6845288