Spectral measures generated by arbitrary and random convolutions

By Dorin Ervin Dutkay, Chun-Kit Lai. 2015

55 citations recorded by the source corpus.

We study spectral measures generated by infinite convolution products of discrete measures generated by Hadamard triples, and we present sufficient conditions for the measures to be spectral, generalizing a criterion by Strichartz. We then study the spectral measures generated by random convolutions of finite atomic measures and rescaling, where the digits are chosen from a finite collection of digit sets. We show that in dimension one, or in higher dimensions under certain conditions, "almost all" such measures generate spectral measures, or, in the case of complete digit sets, translational tiles. Our proofs are based on the study of self-affine spectral measures and tiles generated by Hadamard triples in quasi-product form.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9f8990232595b981cf08b1a3f983e890381ff629

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In Applied Mathematics

1. Li-Xiang An
2. Xiaoye Fu
3. Chun-Kit Lai
4. Xinggang He
5. Xin-Rong Dai
6. J. Miao
7. Wenxia Li
8. Zhiqiang Wang

In Mathematical Physics

1. Li-Xiang An
2. Xiaoye Fu
3. Chun-Kit Lai
4. Xinggang He
5. Xin-Rong Dai
6. Dorin Ervin Dutkay
7. J. Miao
8. Wenxia Li

Citations in the corpus

• On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem (2019, background): “E-mail address: xiaoyefu@mail.ccnu.edu.cn [Chun-Kit Lai]Department of Mathematics, San Francisco State University, 1600 Holloway Avenue, San Francisco, CA 94132.”