Hölder-logarithmic stability in Fourier synthesis. (3rd December 2020) - Isaev, Mikhail; Novikov, Roman G
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.