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.
Funder
Australian Research Council
Subject
Applied Mathematics,Computer Science Applications,Mathematical Physics,Signal Processing,Theoretical Computer Science
Cited by
7 articles.
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