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Licensed Unlicensed Requires Authentication Published by De Gruyter December 11, 2020

Stability estimates for reconstruction from the Fourier transform on the ball

  • Mikhail Isaev ORCID logo EMAIL logo and Roman G. Novikov ORCID logo


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

MSC 2010: 42A38; 35R30; 49K40

Award Identifier / Grant number: DE200101045

Funding statement: The first author’s research is supported by the Australian Research Council Discovery Early Career Researcher Award DE200101045.


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Received: 2020-08-14
Accepted: 2020-10-27
Published Online: 2020-12-11
Published in Print: 2021-06-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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