Spectra of a class of self-affine measures

By Jian-Lin Li. 2011

109 citations recorded by the source corpus.

Abstract In the present paper we will study the spectral property of a class of self-affine measures under the condition of compatible pair. We first answer a question of Dutkay and Jorgensen concerning the relationship between spectral self-affine measure and compatible pair. We then consider the spectra of Bernoulli convolutions and obtain a sharp result which extends the corresponding result of Jorgensen, Kornelson and Shuman. Finally, we provide a structural property for the integer spectrum of a spectral self-affine measure.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8288497ea9ae48b4a62594092bcdce38cf6aa752

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In Applied Mathematics

1. Xin-Rong Dai
2. Qiyu Sun
3. Xinggang He
4. Chun-Kit Lai
5. Li-Xiang An
6. Xiaoye Fu
7. Ka-Sing Lau
8. Liu He

In Mathematical Physics

1. Xin-Rong Dai
2. Qiyu Sun
3. Xinggang He
4. Chun-Kit Lai
5. Li-Xiang An
6. Xiaoye Fu
7. Ka-Sing Lau
8. Liu He

Citations in the corpus

• Spectral measures with arbitrary Hausdorff dimensions (2014, background): “Since then, various singular spectral measures on self-similar/self-affine fractal sets have been found, see for instance [3–6,9,11,15–17,19,21,22,24,26,27,30,34].”