Hölder-logarithmic stability in Fourier synthesis

Mikhail Isaev; Roman G. Novikov

doi:10.1088/1361-6420/abb5df

Hölder-logarithmic stability in Fourier synthesis

Mikhail Isaev
, Roman G. Novikov

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

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 language	English
Article number	125003
Journal	Inverse Problems
Volume	36
Issue number	12
DOIs	https://doi.org/10.1088/1361-6420/abb5df
Publication status	Published - 1 Dec 2020

Keywords

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

Access to Document

10.1088/1361-6420/abb5df

Cite this

@article{06fd2357740e4b2fba0e5869796d42c0,

title = "H{\"o}lder-logarithmic stability in Fourier synthesis",

abstract = "We prove a H{\"o}lder-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 H{\"o}lder 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.",

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

author = "Mikhail Isaev and Novikov, \{Roman G.\}",

note = "Publisher Copyright: {\textcopyright} 2020 IOP Publishing Ltd.",

year = "2020",

month = dec,

day = "1",

doi = "10.1088/1361-6420/abb5df",

language = "English",

volume = "36",

journal = "Inverse Problems",

issn = "0266-5611",

number = "12",

}

TY - JOUR

T1 - Hölder-logarithmic stability in Fourier synthesis

AU - Isaev, Mikhail

AU - Novikov, Roman G.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - 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.

AB - 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.

KW - Analytic extrapolation

KW - Chebyshev approximation

KW - Exponential instability

KW - Hölder-logarithmic stability

KW - Ill-posed inverse problems

U2 - 10.1088/1361-6420/abb5df

DO - 10.1088/1361-6420/abb5df

M3 - Article

AN - SCOPUS:85097868780

SN - 0266-5611

VL - 36

JO - Inverse Problems

JF - Inverse Problems

IS - 12

M1 - 125003

ER -

Hölder-logarithmic stability in Fourier synthesis

Abstract

Keywords

Access to Document

Fingerprint

Cite this