Stability estimates for reconstruction from the Fourier transform on the ball

Mikhail Isaev, Roman G. Novikov

Research output: Contribution to journalArticleResearchpeer-review

Abstract

We prove Hader-logarithmic stability estimates for the problem of finding an integrable function v on Rdwith a super-exponential decay at infinity from its Fourier transform Fv given on the ball Br. These estimates arise from a Halder-stable extrapolation of Fvfrom Br to a larger ball. We also present instability examples showing an optimality of our results.

Original languageEnglish
Number of pages13
JournalJournal of Inverse and Ill-Posed Problems
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • Chebyshev extrapolation
  • Exponential instability
  • Hölder-logarithmic stability
  • Ill-posed inverse problems

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