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

16 Jul 2021  ·  Mikhail Isaev, Roman G. Novikov ·

We give new formulas for finding a compactly supported function $v$ on $\mathbb{R}^d$, $d\geq 1$, from its Fourier transform $\mathcal{F} v$ given within the ball $B_r$. For the one-dimensional case, these formulas are based on the theory of prolate spheroidal wave functions (PSWFs)... In multidimensions, well-known results of the Radon transform theory reduce the problem to the one-dimensional case. Related results on stability and convergence rates are also given. read more

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Classical Analysis and ODEs 42A38, 35R30, 49K40