  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.
