Spectrality of a class of infinite convolutions
Publication in refereed journal

香港中文大學研究人員

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摘要For 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.
著者An LX, He XG, Lau KS
期刊名稱Advances in Mathematics
出版年份2015
月份10
日期1
卷號283
出版社ACADEMIC PRESS INC ELSEVIER SCIENCE
頁次362 - 376
國際標準期刊號0001-8708
電子國際標準期刊號1090-2082
語言英式英語
關鍵詞Admissible pairs; Compatible pairs; Convolution of measures; Moran measures; Self-similar measures; Spectral measures; Universally admissible
Web of Science 學科類別Mathematics

上次更新時間 2021-28-02 於 01:31