Geodesic
Optimal recovery of linear operators in non-Euclidean metrics
Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1442-1472

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

The paper looks at problems concerning the recovery of operators from noisy information in non-Euclidean metrics. A number of general theorems are proved and applied to recovery problems for functions and their derivatives from the noisy Fourier transform. In some cases, a family of optimal methods is found, from which the methods requiring the least amount of original information are singled out. Bibliography: 25 titles. 
@article{SM_2014_205_10_a3,
     author = {K. Yu. Osipenko},
     title = {Optimal recovery of linear operators in {non-Euclidean} metrics},
     journal = {Sbornik. Mathematics},
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     number = {10},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2014_205_10_a3/}
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K. Yu. Osipenko. Optimal recovery of linear operators in non-Euclidean metrics. Sbornik. Mathematics, Tome 205 (2014) no. 10, pp. 1442-1472. http://geodesic.mathdoc.fr/item/SM_2014_205_10_a3/