Stability estimates for reconstruction from the Fourier transform on the ball

Mikhail Isaev; Roman G. Novikov

doi:10.1515/jiip-2020-0106

Stability estimates for reconstruction from the Fourier transform on the ball

Mikhail Isaev
, Roman G. Novikov

Monash University
IEPT RAS

Research output: Contribution to journal › Article › peer-review

Abstract

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

Original language	English
Pages (from-to)	421-433
Number of pages	13
Journal	Journal of Inverse and Ill-Posed Problems
Volume	29
Issue number	3
DOIs	https://doi.org/10.1515/jiip-2020-0106
Publication status	Published - 1 Jun 2021

Keywords

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

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title = "Stability estimates for reconstruction from the Fourier transform on the ball",

abstract = "We prove H{\"o}lder-logarithmic stability estimates for the problem of finding an integrable function v on ℝd with a super-exponential decay at infinity from its Fourier transform Fv given on the ball Br. These estimates arise from a H{\"o}lder-stable extrapolation of Fv from Br to a larger ball. We also present instability examples showing an optimality of our results.",

keywords = "Chebyshev extrapolation, Exponential instability, H{\"o}lder-logarithmic stability, Ill-posed inverse problems",

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T1 - Stability estimates for reconstruction from the Fourier transform on the ball

AU - Isaev, Mikhail

AU - Novikov, Roman G.

PY - 2021/6/1

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N2 - We prove Hölder-logarithmic stability estimates for the problem of finding an integrable function v on ℝd with a super-exponential decay at infinity from its Fourier transform Fv given on the ball Br. These estimates arise from a Hölder-stable extrapolation of Fv from Br to a larger ball. We also present instability examples showing an optimality of our results.

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

KW - Chebyshev extrapolation

KW - Exponential instability

KW - Hölder-logarithmic stability

KW - Ill-posed inverse problems

U2 - 10.1515/jiip-2020-0106

DO - 10.1515/jiip-2020-0106

M3 - Article

AN - SCOPUS:85097906023

SN - 0928-0219

VL - 29

SP - 421

EP - 433

JO - Journal of Inverse and Ill-Posed Problems

JF - Journal of Inverse and Ill-Posed Problems

IS - 3

ER -

Stability estimates for reconstruction from the Fourier transform on the ball

Abstract

Keywords

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