The degree of Copositive approximation by polynomials

D. Leviatan

doi:10.1090/S0002-9939-1983-0691286-7

The degree of Copositive approximation by polynomials

D. Leviatan^*

^*Corresponding author for this work

School of Mathematical Sciences

University of Connecticut

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

12 Scopus citations

Abstract

Jackson type theorems are established for the approximation of a function ƒ that changes sign finitely many times in [-1, 1] by polynomials p_n which are copositive with it (i.e. ƒ_pn ≥ 0 on [-1, 1]). The results yield the rate of noncon-strained approximation and are thus best possible in the same sense as in the nonconstrained case.

Original language	English
Pages (from-to)	101-105
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	88
Issue number	1
DOIs	https://doi.org/10.1090/S0002-9939-1983-0691286-7
State	Published - May 1983

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AB - Jackson type theorems are established for the approximation of a function ƒ that changes sign finitely many times in [-1, 1] by polynomials pn which are copositive with it (i.e. ƒpn ≥ 0 on [-1, 1]). The results yield the rate of noncon-strained approximation and are thus best possible in the same sense as in the nonconstrained case.

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The degree of Copositive approximation by polynomials

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