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arXiv · 2107.07882

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

Mikhail Isaev·Roman G. Novikov
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Abstract

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.

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Mikhail Isaev, Roman G. Novikov. 2021-07-16. Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions. https://arxiv.org/abs/2107.07882

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