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arXiv · 2212.05678

The system of translates and the special affine Fourier transform

Md Hasan Ali Biswas·Frank Filbir·Radha Ramakrishnan
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Abstract

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.

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Md Hasan Ali Biswas, Frank Filbir, Radha Ramakrishnan. 2022-12-12. The system of translates and the special affine Fourier transform. https://arxiv.org/abs/2212.05678

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