Geodesic
Optimal recovery in weighted spaces with homogeneous weights
Sbornik. Mathematics, Tome 213 (2022) no. 3, pp. 385-411

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

The paper concerns problems of the recovery of operators from noisy information in weighted $L_q$-spaces with homogeneous weights. A number of general theorems are proved and applied to problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of the Laplace operator from a noisy Fourier transform in the $L_p$-metric. Bibliography: 30 titles.
Keywords: optimal recovery, linear operator, Carlson's inequality.
Mots-clés : Fourier transform 
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     author = {K. Yu. Osipenko},
     title = {Optimal recovery in weighted spaces with homogeneous weights},
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K. Yu. Osipenko. Optimal recovery in weighted spaces with homogeneous weights. Sbornik. Mathematics, Tome 213 (2022) no. 3, pp. 385-411. http://geodesic.mathdoc.fr/item/SM_2022_213_3_a5/