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

Mikhail Isaev; Roman G. Novikov

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

Classical Analysis and ODEs 2021-07-19 v1

Authors: Mikhail Isaev , Roman G. Novikov

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.

Keywords

fourier transform prolate spheroidal wave functions compactly supported function radon transform reconstruction stability convergence rates

Cite

@article{arxiv.2107.07882,
  title  = {Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions},
  author = {Mikhail Isaev and Roman G. Novikov},
  journal= {arXiv preprint arXiv:2107.07882},
  year   = {2021}
}

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

Abstract

Keywords

Cite

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