A Lower Estimate for Entropy Numbers

In this: publication
By this: publisher
In this Subject: <a title="Mathematics and Statistics" href="/content/subcat?j_subject=195&j_availability=">Mathematics and Statistics
By this author: K&uuml;hn T.

Author: Kühn T.

Source: Journal of Approximation Theory, Volume 110, Number 1, May 2001 , pp. 120-124(5)

Buy & download fulltext article:

Price: $52.63 plus tax (Refund Policy)

Abstract:

The behaviour of the entropy numbers e_k(id: lⁿ_p rarr lⁿ_q), 0<p<q les infin , is well known (up to multiplicative constants independent of n and k), except in the quasi-Banach case 0<p<1 for “medium size” k, i.e., when log n les k les n, where only an upper estimate is available so far. We close this gap by proving the lower estimate e_k(id: lⁿ_p rarr lⁿ_q) ges c(log(n/k+1)/k)^1/p-1/q for all 0<p<q les infin and log n les k les n, with some constant c>0 depending only on p. Copyright 2001 Academic Press.