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arXiv · 2007.12013

Stability estimates for reconstruction from the Fourier transform on the ball

Mikhail Isaev·Roman G. Novikov
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Abstract

We prove H\"{o}lder-logarithmic stability estimates for the problem of finding an integrable function $v$ on $\mathbb{R}^d$ with a super-exponential decay at infinity from its Fourier transform $\mathcal{F} v$ given on the ball $B_r$. These estimates arise from a H\"{o}lder-stable extrapolation of $\mathcal{F} v$ from $B_r$ to a larger ball. We also present instability examples showing an optimality of our results.

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Mikhail Isaev, Roman G. Novikov. 2020-07-23. Stability estimates for reconstruction from the Fourier transform on the ball. https://arxiv.org/abs/2007.12013

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