Copositive approximation by rational functions with prescribed numerator degree

The paper proves that, if f ( x ) ∈ L [−1,1] p , 1 ≤ p < ∞, changes sign l times in (−1, 1), then there exists a real rational function r ( x ) ∈ R n (2 μ −1) l which is copositive with f ( x ), such that the following Jackson type estimate holds, where μ is a natural number ≥ 3/2 + 1/ p , and C...

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Bibliographic Details
Published inApplied Mathematics-A Journal of Chinese Universities Vol. 24; no. 4; pp. 411 - 416
Main Authors Yu, Dan-sheng, Zhou, Song-ping
Format Journal Article
LanguageEnglish
Published Heidelberg SP Editorial Committee of Applied Mathematics - A Journal of Chinese Universities 01.12.2009
Subjects
Applications of Mathematics
Mathematics
Mathematics and Statistics
approximation rate
rational functions
copositive approximation
41A30
41A20
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Summary:The paper proves that, if f ( x ) ∈ L [−1,1] p , 1 ≤ p < ∞, changes sign l times in (−1, 1), then there exists a real rational function r ( x ) ∈ R n (2 μ −1) l which is copositive with f ( x ), such that the following Jackson type estimate holds, where μ is a natural number ≥ 3/2 + 1/ p , and C δ is a positive constant depending only on δ .
ISSN:1005-1031
1993-0445
DOI:10.1007/s11766-009-2076-5