Geodesic
Best recovery of the Laplace operator of a function from incomplete spectral data
Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 569-580 Cet article a éte moissonné depuis la source Math-Net.Ru

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This paper is concerned with the problem of best recovery for a fractional power of the Laplacian of a smooth function on $\mathbb R^d$ from an exact or approximate Fourier transform for it, which is known on some convex subset of $\mathbb R^d$. A series of optimal recovery methods is constructed. Information about the Fourier transform outside some ball centred at the origin proves redundant — it is not used by the optimal methods. These optimal methods differ in the way they ‘process’ key information. Bibliography: 12 titles.
Keywords: Laplace operator, optimal recovery, extremal problem
Mots-clés : Fourier transform. 
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G. G. Magaril-Il'yaev; E. O. Sivkova. Best recovery of the Laplace operator of a function from incomplete spectral data. Sbornik. Mathematics, Tome 203 (2012) no. 4, pp. 569-580. http://geodesic.mathdoc.fr/item/SM_2012_203_4_a5/

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