Hölder-logarithmic stability in Fourier synthesis

Abstract

We prove a Hölder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function $v$ on ${\mathbb{R}}^d$ from its Fourier transform $\mathcal{F}v$ given on $[-r,r{]}^d$. This estimate relies on a Hölder stable continuation of $\mathcal{F}v$ from $[-r,r{]}^d$ to a larger domain. The related reconstruction procedures are based on truncated series of Chebyshev polynomials. We also give an explicit example showing optimality of our stability estimates.

References in corpus (4)

• New global stability estimates for the Gel'fand-Calderon inverse problem
• Variational source conditions and stability estimates for inverse electromagnetic medium scattering problems
• Effectivized Holder-logarithmic stability estimates for the Gel'fand inverse problem
• Energy and regularity dependent stability estimates for near-field inverse scattering in multidimensions

Cited by in corpus (2)

• Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions
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