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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.24165 |
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| _version_ | 1866908913189781504 |
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| author | Rible, Quentin Seuret, Stéphane |
| author_facet | Rible, Quentin Seuret, Stéphane |
| contents | We prove that, given a wavelet $ψ$, it is possible to choose some multi-integers $(p_j=(p_{j,1},...,p_{j,d}))_{j \in \mathbb{Z}} \in \mathbb{Z}^d$ such that, for every $x=(x_1,...,x_d) \in \mathbb{R}^d$, for infinitely many integers $j$, the tensorized wavelet $\prod_{i=1}^d ψ(2^j x_i-p_{j,i})$ does not vanish at $x$. This non-vanishing property is essential for analyzing some generic regularity properties in certain Sobolev and Besov spaces. The proof relies on an assumption regarding the zeros of $ψ$, which we numerically verify for the first Daubechies wavelets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24165 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A non-vanishing property for tensor products of wavelets Rible, Quentin Seuret, Stéphane Functional Analysis We prove that, given a wavelet $ψ$, it is possible to choose some multi-integers $(p_j=(p_{j,1},...,p_{j,d}))_{j \in \mathbb{Z}} \in \mathbb{Z}^d$ such that, for every $x=(x_1,...,x_d) \in \mathbb{R}^d$, for infinitely many integers $j$, the tensorized wavelet $\prod_{i=1}^d ψ(2^j x_i-p_{j,i})$ does not vanish at $x$. This non-vanishing property is essential for analyzing some generic regularity properties in certain Sobolev and Besov spaces. The proof relies on an assumption regarding the zeros of $ψ$, which we numerically verify for the first Daubechies wavelets. |
| title | A non-vanishing property for tensor products of wavelets |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2603.24165 |