2000 character limit reached
The system of translates and the special affine Fourier transform (2212.05678v2)
Published 12 Dec 2022 in math.FA
Abstract: The translation operator $TA$ 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.