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.

MSC: 41A10

Received: 31.08.2011

Language: English

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