Hardy's theorem for the q-Bessel Fourier transform
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2007
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| _version_ | 1866918494220582912 |
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| author | Dhaouadi, Lazhar |
| author_facet | Dhaouadi, Lazhar |
| contents | In this paper we give a q-analogue of the Hardy's theorem for the $q$-Bessel Fourier transform. The celebrated theorem asserts that if a function $f$ and its Fourier transform $\hat{f}$ satisfying $|f(x)|\leq c.e^{-{1/2} x^2}$ and $|\hat{f}(x)|\leq c.e^{-{1/2} x^2}$ for all $x\in\mathbb{% R}$ then $f(x)=\text{const}.e^{-{1/2} x^2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0707_2346 |
| institution | arXiv |
| publishDate | 2007 |
| record_format | arxiv |
| spellingShingle | Hardy's theorem for the q-Bessel Fourier transform Dhaouadi, Lazhar Classical Analysis and ODEs In this paper we give a q-analogue of the Hardy's theorem for the $q$-Bessel Fourier transform. The celebrated theorem asserts that if a function $f$ and its Fourier transform $\hat{f}$ satisfying $|f(x)|\leq c.e^{-{1/2} x^2}$ and $|\hat{f}(x)|\leq c.e^{-{1/2} x^2}$ for all $x\in\mathbb{% R}$ then $f(x)=\text{const}.e^{-{1/2} x^2}$. |
| title | Hardy's theorem for the q-Bessel Fourier transform |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/0707.2346 |