Geodesic
Optimal recovery of functions and their derivatives from Fourier coefficients
Sbornik. Mathematics, Tome 193 (2002) no. 3, pp. 387-407

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The problems of the optimal recovery of functions and their derivatives from approximate values of their Fourier coefficients are considered. Explicit expressions for optimal recovery methods in classes of smooth and analytic functions defined on various compact manifolds are presented. 
@article{SM_2002_193_3_a5,
     author = {G. G. Magaril-Il'yaev and K. Yu. Osipenko},
     title = {Optimal recovery of functions and their derivatives from {Fourier} coefficients},
     journal = {Sbornik. Mathematics},
     pages = {387--407},
     publisher = {mathdoc},
     volume = {193},
     number = {3},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2002_193_3_a5/}
}
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G. G. Magaril-Il'yaev; K. Yu. Osipenko. Optimal recovery of functions and their derivatives from Fourier coefficients. Sbornik. Mathematics, Tome 193 (2002) no. 3, pp. 387-407. http://geodesic.mathdoc.fr/item/SM_2002_193_3_a5/