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Zh. Mat. Fiz. Anal. Geom., 2012, Volume 8, Number 1, Pages 63–78 (Mi jmag525)  

Elementary solutions of the Bernstein problem on two intervals

F. Pausinger

I.S.T. Austria, Am Campus 1, A-3400 Klosterneuburg, Austria

Abstract: First we note that the best polynomial approximation to $|x|$ on the set, which consists of an interval on the positive half-axis and a point on the negative half-axis, can be given by means of the classical Chebyshev polynomials. Then we explore the cases when a solution of the related problem on two intervals can be given in elementary functions.

Key words and phrases: Chebyshev polynomials, polynomial approximation of $|x|$, Bernstein problem.

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Bibliographic databases:
MSC: 41A10
Received: 31.08.2011
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Citation: F. Pausinger, “Elementary solutions of the Bernstein problem on two intervals”, Zh. Mat. Fiz. Anal. Geom., 8:1 (2012), 63–78

Citation in format AMSBIB
\Bibitem{Pau12}
\by F. Pausinger
\paper Elementary solutions of the Bernstein problem on two intervals
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2012
\vol 8
\issue 1
\pages 63--78
\mathnet{http://mi.mathnet.ru/jmag525}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2963010}
\zmath{https://zbmath.org/?q=an:06082845}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000301173600004}


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