Approximation by polynomials and ridge functions of classes of s-monotone radial functions

doi:10.1016/j.jat.2007.10.001

Journal of Approximation Theory

Volume 152, Issue 1, May 2008, Pages 20-51

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Abstract

We obtain estimates on the order of best approximation by polynomials and ridge functions in the spaces $L_{q}$ of classes of s-monotone radial functions which belong to the space $L_{p}$ , $1 ⩽ q ⩽ p \leq \infty$ .

MSC

41A46

Keywords

s

-Monotone functions

Radial functions

Polynomials

Ridge functions

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¹: Part of this work was done while the first author visited Tel Aviv University and Technion I.I.T. Haifa in January 2005 and June 2006.