Geodesic
The best approximation of a~set whose elements are known approximately
Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 5, pp. 127-141

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This paper is concerned with the problem of the best (in a precisely defined sense) approximation with given accuracy of periodic functions and functions on the real line from, respectively, a finite tuple of noisy Fourier coefficients or noisy Fourier transform on an arbitrary set of finite measure. 
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     author = {G. G. Magaril-Il'yaev and K. Yu. Osipenko and E. O. Sivkova},
     title = {The best approximation of a~set whose elements are known approximately},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {127--141},
     publisher = {mathdoc},
     volume = {19},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2014_19_5_a5/}
}
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G. G. Magaril-Il'yaev; K. Yu. Osipenko; E. O. Sivkova. The best approximation of a~set whose elements are known approximately. Fundamentalʹnaâ i prikladnaâ matematika, Tome 19 (2014) no. 5, pp. 127-141. http://geodesic.mathdoc.fr/item/FPM_2014_19_5_a5/