Spectral measures with arbitrary Hausdorff dimensions

By Xin-Rong Dai, Qiyu Sun. 2014

52 citations recorded by the source corpus.

In this paper, we consider spectral properties of Riesz product measures supported on homogeneous Cantor sets and we show the existence of spectral measures with arbitrary Hausdorff dimensions, including non-atomic zero-dimensional spectral measures and one-dimensional singular spectral measures.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/71bc538273b00f91be0ea2f9c18a5115def983f4

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In Applied Mathematics

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

In Computational Theory and Mathematics

1. Li-Xiang An
2. Chun-Kit Lai
3. Xiaoye Fu
4. J. Miao
5. Wenxia Li
6. Zhiqiang Wang

In Mathematical Physics

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

Citations in the corpus

• Weak convergence and spectrality of infinite convolutions (2022, result): “The similar result for spectral measures with compact support has been proved in [13].”
• On spectral Cantor-Moran measures and a variant of Bourgain's sum of sine problem (2019, background): “These Cantor-Moran measures also show that spectral measures can have support of any Hausdorff dimensions [12].”