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DOI: 10.23671/VNC.2012.14.11012

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
Language: Russian Download the full text  
For citation: †Sivkova E. O. On optimal recovery of the Laplacian of a function from its inaccurately given Fourier transform. Vladikavkazskij matematicheskij zhurnal [Vladikavkaz Math. J.],† 2012, vol. 14, no. 4, pp.63-72. DOI 10.23671/VNC.2012.14.11012


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