Hölder-logarithmic stability in Fourier synthesis. (3rd December 2020)

• Record Type: Journal Article
• Authors: Isaev, Mikhail; Novikov, Roman G
• Is Part Of: Inverse problems. Volume 36:Number 12(2020)
• Publication Date: 2020-12-03
• Subjects: ill-posed inverse problems -- Hölder-logarithmic stability -- exponential instability -- Chebyshev approximation -- analytic extrapolation; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/abb5df
• Languages: English
• ISSNs: 0266-5611

Abstract

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