Polynomials of fixed sign that deviate least from zero in the spaces LP

descriptionPublicationkeyboard_double_arrow_right Article 01 Feb 1985 English Publisher:Springer Science and Business Media LLCJournal:Mathematical Notes of the Academy of Sciences of the USSR, volume 37, pages 99-105 (issn: 0001-4346, eissn: 1573-8876,

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Authors: Babenko, V. F.; Kofanov, V. A.;

doi: 10.1007/bf01156752

Polynomials of fixed sign that deviate least from zero in the spaces LP

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Abstract

It is proved that the finding of polynomials of constants signs of least deviation from zero in spaces \(L_ p\) with weight may be reduced to the similar problem on arbitrary polynomials but for other metric and other weight. This result generalizes one result of \textit{R. Bojanic} and \textit{R. De Vore} [Enseign. Math., II. Ser. 12, 139-164 (1966; Zbl 0152.256)].

Keywords

Best approximation, Chebyshev systems, Approximation by polynomials, polynomials of constants signs, weight

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