Geodesic
On optimal recovery of the Laplacian of a~function from its inaccurately given Fourier transform
Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 63-72

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The paper is devoted to the problem of the optimal recovery for a fractional power of the Laplacian of a function from its inaccurately given Fourier transform in metric $L_\infty$ on some convex subset of $\mathbb R^d$. The optimal recovery method is constructed. This method is not used the information about the Fourier transform outside some ball centred at the origin. 
@article{VMJ_2012_14_4_a8,
     author = {E. O. Sivkova},
     title = {On optimal recovery of the {Laplacian} of a~function from its inaccurately given {Fourier} transform},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {63--72},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a8/}
}
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E. O. Sivkova. On optimal recovery of the Laplacian of a~function from its inaccurately given Fourier transform. Vladikavkazskij matematičeskij žurnal, Tome 14 (2012) no. 4, pp. 63-72. http://geodesic.mathdoc.fr/item/VMJ_2012_14_4_a8/