Spectra of Bernoulli convolutions and random convolutions

By Yan-Song Fu, Xinggang He, Zhi-Xiong Wen. Journal des Mathématiques Pures et Appliquées, 2018

99 citations recorded by the source corpus.

Abstract In this work we study the harmonic analysis of infinite convolutions generated by compatible pairs. We first give some sufficient conditions so that a random infinite convolution μ becomes a spectral measure, i.e., there exists a countable set Λ ⊆ R n such that E ( Λ ) = { e 2 π i 〈 λ , x 〉 : λ ∈ Λ } forms an orthonormal basis for L 2 ( μ ) . As applications, we settle down the spectral eigenvalue problem for spectral Bernoulli convolutions.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ba6d4931349109369dbb1432aaf639ab44cdf48c

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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): “measures [9, 10, 11], as well as the convergence properties of the associated Fourier series [38, 39, 13] and the rescaling properties of a given spectrum [19, 16, 21].”