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 Vladikavkaz. Mat. Zh., 2012, Volume 14, Number 4, Pages 63–72 (Mi vmj438)

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

E. O. Sivkova

Moscow State Institute of Radio-Engineering, Electronics and Automation (Technical University), Russia, Moscow

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.

Key words: optimal recovery, Laplacian, Fourier transform, convex problem.

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Citation: E. O. Sivkova, “On optimal recovery of the Laplacian of a function from its inaccurately given Fourier transform”, Vladikavkaz. Mat. Zh., 14:4 (2012), 63–72

Citation in format AMSBIB
\Bibitem{Siv12} \by E.~O.~Sivkova \paper On optimal recovery of the Laplacian of a~function from its inaccurately given Fourier transform \jour Vladikavkaz. Mat. Zh. \yr 2012 \vol 14 \issue 4 \pages 63--72 \mathnet{http://mi.mathnet.ru/vmj438} 

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This publication is cited in the following articles:
1. G. G. Magaril-Il'yaev, K. Yu. Osipenko, “On best harmonic synthesis of periodic functions”, J. Math. Sci., 209:1 (2015), 115–129
2. E. O. Sivkova, “Best recovery of the Laplace operator of a function and sharp inequalities”, J. Math. Sci., 209:1 (2015), 130–137
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