On spectral N-Bernoulli measures
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AbstractFor 0 < rho < 1 and N > 1 an integer, let mu be the self-similar measure defined by mu(center dot) = Sigma(N-1)(i=0) 1/N mu(rho(-1)(center dot) - i). We prove that L-2(mu) has an exponential orthonormal basis if and only if rho = 1/q for some q > 0 and N divides q. The special case is the Cantor measure with rho = 1/2k and N = 2 [16], which was proved recently to be the only spectral measure among the Bernoulli convolutions with 0 < rho < 1 [4]. (C) 2014 Elsevier Inc. All rights reserved.
All Author(s) ListDai XR, He XG, Lau KS
Journal nameAdvances in Mathematics
Volume Number259
Pages511 - 531
LanguagesEnglish-United Kingdom
KeywordsBernoulli convolution; Bi-zero set; Fourier transform; Orthogonal; Self-similar; Spectral measure; Spectrum
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-15-04 at 23:55