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A Class of Homogeneous Moran Spectral Measures with Eight-Element Digit Sets on \({\mathbb R}^4\)

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Abstract

In the present paper we shall investigate the harmonic analysis of a class of singular homogeneous Moran measures \(\mu \) with eight-element digit sets on \({\mathbb R}^4\). Our main results show that these measures \(\mu \) are spectral measures, that is, the associated Hilbert space \(L^2(\mu )\) admits an exponential orthonormal basis.

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Notes

  1. This concept is first introduced by Dutkay, Hausserman and Lai in [4].

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Acknowledgements

The authors would like to thank the anonymous referee for her/his valuable suggestions and comments that greatly improved the presentation of this article.

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Authors and Affiliations

  1. Department of mathematics, China University of Mining and Technology-Beijing, Beijing, 100083, People’s Republic of China

    Yan-Song Fu

  2. School of Mathematics, Sun Yat-Sen university, Guangzhou, 510275, People’s Republic of China

    Meng Zhu

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  1. Yan-Song Fu
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  2. Meng Zhu
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Correspondence to Meng Zhu.

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Fu is supported by the National Natural Science Foundation of China (No. 11801035) and the Fundamental Research Funds for the Central Universities (No. 2021YQLX07). Zhu is supported by the National Natural Science Foundation of China (Nos. 11771457, 11971500) and the Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University.

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Fu, YS., Zhu, M. A Class of Homogeneous Moran Spectral Measures with Eight-Element Digit Sets on \({\mathbb R}^4\). Results Math 76, 207 (2021). https://doi.org/10.1007/s00025-021-01519-x

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