Title

Spectral measures with arbitrary Hausdorff dimensions

Authors

Authors

X. R. Dai;Q. Y. Sun

Comments

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Abbreviated Journal Title

J. Funct. Anal.

Keywords

Spectral measure; Homogeneous Cantor set; Hausdorff dimension; Bernoulli; convolution; SELF-AFFINE TILES; CANTOR MEASURES; FOURIER-SERIES; BASES; SETS; CONJECTURE; PROPERTY; WAVELETS; FRAMES; MOCK; Mathematics

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. (C) 2015 Elsevier Inc. All rights reserved.

Journal Title

Journal of Functional Analysis

Volume

268

Issue/Number

8

Publication Date

1-1-2015

Document Type

Article

DOI Link

http://dx.doi.org/10.1016/j.jfa.2015.01.005

Language

English

First Page

2464

Last Page

2477

WOS Identifier

WOS:000351807700014

ISSN

0022-1236

Recommended Citation

"Spectral measures with arbitrary Hausdorff dimensions" (2015). Faculty Bibliography 2010s. 6485.
https://stars.library.ucf.edu/facultybib2010/6485