Hölder-logarithmic stability in Fourier synthesis

Mikhail Isaev, Roman G. Novikov

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Abstract

We prove a Hölder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function v on Rd from its Fourier transform Fv given on [-r, r]d. This estimate relies on a Hölder stable continuation of Fv 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.

Original languageEnglish
Article number125003
Number of pages17
JournalInverse Problems
Volume36
Issue number12
DOIs
Publication statusPublished - 3 Dec 2020

Keywords

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

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