Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

Mikhail Isaev, Roman G. Novikov

We give new formulas for finding a compactly supported function $v$ on ${\mathbb{R}}^d$, $d\ge 1$, from its Fourier transform $\mathcal{F}v$ given within the ball $B_r$. For the on…