Non-Spectral Problem on Infinite Bernoulli Convolution

Let be an upper-bounded sequence of positive integers and let δ E be the uniformly discrete probability measure on the finite set E . For 0 < ρ < 1, the infinite convolution is called an infinite Bernoulli convolution. The non-spectral problem on is to investigate the cardinality of orthogonal...

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Bibliographic Details
Published in:Analysis mathematica (Budapest) 2021-06, Vol.47 (2), p.343-355
Main Authors: Li, Q., Wu, Z.-Y.
Format: Article
Language:English
Subjects:
Analysis
Convolution
Mathematics
Mathematics and Statistics
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Summary:Let be an upper-bounded sequence of positive integers and let δ E be the uniformly discrete probability measure on the finite set E . For 0 < ρ < 1, the infinite convolution is called an infinite Bernoulli convolution. The non-spectral problem on is to investigate the cardinality of orthogonal exponentials in . In this paper, we give a characterization of this problem by classifying the values of ρ .
ISSN:0133-3852
1588-273X
DOI:10.1007/s10476-021-0069-7