An upper bound on the Kolmogorov widths of a certain family of integral operators

JOURNAL OF APPROXIMATION THEORY

卷:240

Article

Lewis, Duaine¹  Sing, Bernd¹ 

[1] Univ West Indies, Dept Math, Cave Hill,POB 64,BB11000, Bridgetown, St Michael, Barbados

关键词: Kolmogorov widths;    Integral operator;    Entropy numbers;   

DOI  :  10.1016/j.jat.2018.09.012

来源: Elsevier

【 摘 要 】

We consider the family of integral operators (K-alpha f)(x) from L-P [0, 1] to L-q [0, 1] given by (K-alpha f)(x) = integral(1)(0)(1- xy) (alpha-1) f (y) dy, 0 < alpha < 1. The main objective is to find upper bounds for the Kolmogorov widths of these operators; these are then used to derive upper bounds for their entropy numbers. We find upper bounds for the nth Kolmogorov widths in question that decrease faster than exp(-kappa root n), and for the nth entropy numbers that decrease faster than exp(-c (3)root n), for some positive constants kappa and c. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free