Sparse sampling recovery in integral norms on some function classes
Sbornik. Mathematics, Tome 215 (2024) no. 10, pp. 1406-1425
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This paper is a direct followup of a recent paper of the author. We continue to analyze approximation and recovery properties with respect to systems satisfying the universal sampling discretization property and a special unconditionality property. In addition, we assume that the subspace spanned by our system satisfies some Nikol'skii-type inequalities. We concentrate on recovery with an error measured in the $L_p$-norm for $2\le p\infty$. We apply a powerful nonlinear approximation method — the Weak Orthogonal Matching Pursuit (WOMP), also known under the name of the Weak Orthogonal Greedy Algorithm (WOGA). We establish that the WOMP based on good points for $L_2$-universal discretization provides good recovery in the $L_p$-norm for $2\le p\infty$. For our recovery algorithms we obtain both Lebesgue-type inequalities for individual functions and error bounds for special classes of multivariate functions.
We combine two deep and powerful techniques — Lebesgue-type inequalities for the WOMP and the theory of universal sampling discretization — in order to obtain new results on sampling recovery.
Bibliography: 19 titles.
Keywords:
sampling discretization, universality, recovery.
@article{SM_2024_215_10_a4,
author = {V. N. Temlyakov},
title = {Sparse sampling recovery in integral norms on some function classes},
journal = {Sbornik. Mathematics},
pages = {1406--1425},
publisher = {mathdoc},
volume = {215},
number = {10},
year = {2024},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2024_215_10_a4/}
}
V. N. Temlyakov. Sparse sampling recovery in integral norms on some function classes. Sbornik. Mathematics, Tome 215 (2024) no. 10, pp. 1406-1425. http://geodesic.mathdoc.fr/item/SM_2024_215_10_a4/