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

V. N. Konovalov; D. Leviatan; V. E. Maiorov

doi:10.1016/j.jat.2007.10.001

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

V. N. Konovalov, D. Leviatan, V. E. Maiorov

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

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 ≤ ∞.

Original language	English
Pages (from-to)	20-51
Number of pages	32
Journal	Journal of Approximation Theory
Volume	152
Issue number	1
DOIs	https://doi.org/10.1016/j.jat.2007.10.001
State	Published - May 2008

Keywords

Polynomials
Radial functions
Ridge functions
s-Monotone functions

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10.1016/j.jat.2007.10.001

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title = "Approximation by polynomials and ridge functions of classes of s-monotone radial functions",

abstract = "We obtain estimates on the order of best approximation by polynomials and ridge functions in the spaces Lq of classes of s-monotone radial functions which belong to the space Lp, 1 ≤ q ≤ p ≤ ∞.",

keywords = "Polynomials, Radial functions, Ridge functions, s-Monotone functions",

author = "Konovalov, {V. N.} and D. Leviatan and Maiorov, {V. E.}",

year = "2008",

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doi = "10.1016/j.jat.2007.10.001",

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AU - Konovalov, V. N.

AU - Leviatan, D.

AU - Maiorov, V. E.

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N2 - We obtain estimates on the order of best approximation by polynomials and ridge functions in the spaces Lq of classes of s-monotone radial functions which belong to the space Lp, 1 ≤ q ≤ p ≤ ∞.

AB - We obtain estimates on the order of best approximation by polynomials and ridge functions in the spaces Lq of classes of s-monotone radial functions which belong to the space Lp, 1 ≤ q ≤ p ≤ ∞.

KW - Polynomials

KW - Radial functions

KW - Ridge functions

KW - s-Monotone functions

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JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

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

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Keywords

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