The system of translates and the special affine Fourier transform
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909262464155648 |
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| author | Biswas, Md Hasan Ali Filbir, Frank Ramakrishnan, Radha |
| author_facet | Biswas, Md Hasan Ali Filbir, Frank Ramakrishnan, Radha |
| contents | The translation operator $T^A$ associated with the special affine Fourier transform (SAFT) $\mathscr{F}_A$ is introduced from harmonic analysis point of view. The analogues of Wendel's theorem, Wiener theorem, Weiner-Tauberian theorem and Bernstein type inequality in the context of the SAFT are established. The shift invariant space $V_A$ associated with the special affine Fourier transform is introduced and studied along with sampling problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05678 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The system of translates and the special affine Fourier transform Biswas, Md Hasan Ali Filbir, Frank Ramakrishnan, Radha Functional Analysis Primary 42A38, Secondary 42A85, 42C15 The translation operator $T^A$ associated with the special affine Fourier transform (SAFT) $\mathscr{F}_A$ is introduced from harmonic analysis point of view. The analogues of Wendel's theorem, Wiener theorem, Weiner-Tauberian theorem and Bernstein type inequality in the context of the SAFT are established. The shift invariant space $V_A$ associated with the special affine Fourier transform is introduced and studied along with sampling problems. |
| title | The system of translates and the special affine Fourier transform |
| topic | Functional Analysis Primary 42A38, Secondary 42A85, 42C15 |
| url | https://arxiv.org/abs/2212.05678 |