Spectrality of a class of infinite convolutions
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AbstractFor a finite set D subset of Z and an integer b >= 2, we say that (b, D) is compatible with C subset of Z if [e(-2 pi id/b)](d is an element of D,c is an element of C) is a Hadainard. matrix. Let delta(E) = 1/#E Sigma(a is an element of E) delta(a) denote the uniformly discrete probability measure on E. We prove that the class of infinite convolution (Moran measure) mu(b),{D-k} = delta(b)-1D(1) *delta(b-2D2) * center dot center dot center dot is a spectral measure provided that there is a common C subset of Z(+) compatible to all the (b, D-k) and C + C subset of {0,1, ... , b - 1}. We also give some examples to illustrate the hypotheses and results, in particular, the last condition on C is essential. (C) 2015 Elsevier Inc. All rights reserved.
All Author(s) ListAn LX, He XG, Lau KS
Journal nameAdvances in Mathematics
Volume Number283
Pages362 - 376
LanguagesEnglish-United Kingdom
KeywordsAdmissible pairs; Compatible pairs; Convolution of measures; Moran measures; Self-similar measures; Spectral measures; Universally admissible
Web of Science Subject CategoriesMathematics

Last updated on 2021-15-01 at 00:41