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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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