On optimal recovery of the Laplacian of a function from its inaccurately given Fourier transform

Sivkova E. O.
Vladikavkaz Mathematical Journal 2012. Vol. 14. Issue 4.

Abstract:
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.

Keywords: optimal recovery, Laplacian, Fourier transform, convex problem

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