Geodesic
How Best to Recover a Function from Its Inaccurately Given Spectrum?
Matematičeskie zametki, Tome 92 (2012) no. 1, pp. 59-67

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Consider the problem of optimal recovery of a function and its derivatives on the line from the Fourier transform of the function known approximately on a set of finite measure. We find an optimal recovery method and an optimal set on which we must measure the Fourier transform with given error.
Keywords: optimal recovery of a function, Sobolev class of functions, Lagrange function.
Mots-clés : Fourier transform 
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G. G. Magaril-Il'yaev; K. Yu. Osipenko. How Best to Recover a Function from Its Inaccurately Given Spectrum?. Matematičeskie zametki, Tome 92 (2012) no. 1, pp. 59-67. http://geodesic.mathdoc.fr/item/MZM_2012_92_1_a5/