Spectral Measures With Arbitrary Hausdorff Dimensions

Keywords

Bernoulli convolution; Hausdorff dimension; Homogeneous Cantor set; Spectral measure

Abstract

In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.

Publication Date

4-15-2015

Publication Title

Journal of Functional Analysis

Volume

268

Issue

8

Number of Pages

2464-2477

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.jfa.2015.01.005

Socpus ID

84924217414 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84924217414

This document is currently not available here.

Share

COinS