Spectrality of one dimensional self-similar measures with consecutive digits

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Deng, Qi-Rong

关键词: Spectral measure;    Self-similar measure;    Consecutive digits;   

DOI  :  10.1016/j.jmaa.2013.07.046

来源: Elsevier

【 摘 要 】

Assume 0 < vertical bar rho vertical bar < 1 and m is a prime, let mu(rho) be the self-similar measure defined by mu(rho) (A) = 1/m Sigma(m-1)(j=0) mu(rho) (rho-1 A - j), for all A epsilon B. We prove that L-2(mu(rho)) contains an orthonormal basis of exponential functions if and only if rho = +/- 1/mk for some k epsilon N. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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