Journal of Approximation Theory
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 J. Approx. Theory, 2013, Volume 173, Pages 110–121 (Mi jath3)

An inequality for the entropy numbers and its application

V. N. Temlyakovab

a Steklov Institute of Mathematics, Russia
b University of South Carolina, United States

Abstract: We prove an inequality for the entropy numbers in terms of nonlinear Kolmogorov widths. This inequality is in the spirit of known inequalities of this type and it is adjusted to a form convenient in applications for $m$-term approximations with respect to a given system. Also, we obtain upper bounds for the $m$-term approximation by using the Weak Relaxed Greedy Algorithm with respect to a system which is not a dictionary.

 Funding Agency Grant Number National Science Foundation DMS-1160841 Author's research was supported by NSF grant DMS-1160841.

DOI: https://doi.org/10.1016/j.jat.2013.05.003

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Accepted:13.05.2013
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