The Spectrality of Infinite Convolutions in $\mathbb{R}^d$
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866929544223522816 |
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| author | Li, Wenxia Wang, Zhiqiang |
| author_facet | Li, Wenxia Wang, Zhiqiang |
| contents | 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 $\mathbb{R}^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_08462 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The Spectrality of Infinite Convolutions in $\mathbb{R}^d$ Li, Wenxia Wang, Zhiqiang Classical Analysis and ODEs Functional Analysis 28A80, 42B05, 42C30 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 $\mathbb{R}^d$. |
| title | The Spectrality of Infinite Convolutions in $\mathbb{R}^d$ |
| topic | Classical Analysis and ODEs Functional Analysis 28A80, 42B05, 42C30 |
| url | https://arxiv.org/abs/2210.08462 |