Spectral measures with arbitrary Hausdorff dimensions

    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

    Language

    English

    First Page

    2464

    Last Page

    2477

    WOS Identifier

    WOS:000351807700014

    ISSN

    0022-1236

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