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arXiv · 2210.08462

The Spectrality of Infinite Convolutions in $\mathbb{R}^d$

Wenxia Li·Zhiqiang Wang
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Abstract

In this paper, we study the spectrality of infinite convolutions in $\mathbb{R}^d$, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. Suppose that the infinite convolutions are generated by a sequence of admissible pairs in $\mathbb{R}^d$. We give two sufficient conditions for their spectrality by using the equi-positivity condition and the integral periodic zero set of Fourier transform. By applying these results, we show the spectrality of some specific infinite convolutions in $\mathbb{R}^d$.

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BibTeXRIS

Wenxia Li, Zhiqiang Wang. 2022-10-16. The Spectrality of Infinite Convolutions in $\mathbb{R}^d$. https://doi.org/10.1007/s00041-024-10094-y

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