Holder-logarithmic stability in Fourier synthesis

被引：6
|
作者：
Isaev, Mikhail [1 ]
Novikov, Roman G. [2 ,3 ]
机构：
[1] Monash Univ Clayton, Sch Math, Clayton, Vic, Australia
[2] Inst Polytech Paris Palaiseau, Ecole Polytech, CNRS, CMAP, Palaiseau, France
[3] IEPT RAS, Moscow 117997, Russia
来源：
INVERSE PROBLEMS | 2020年 / 36卷 / 12期
基金：
澳大利亚研究理事会;
关键词：
ill-posed inverse problems; Holder-logarithmic stability; exponential instability; Chebyshev approximation; analytic extrapolation; EXPONENTIAL INSTABILITY; INVERSE; EXTRAPOLATION;
D O I：
10.1088/1361-6420/abb5df
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove a Holder-logarithmic stability estimate for the problem of finding a sufficiently regular compactly supported function v on R-d from its Fourier transform Fv given on [-r, r](d). This estimate relies on a Holder 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.
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页数：17
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