Document Zbl 1150.41346

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One condition for a polynomial which is sufficient for the polynomial norm minimality on given compact. (Russian, English) Zbl 1150.41346

Vestn. Mosk. Univ., Ser. I 2006, No. 4, 14-18 (2006); translation in Mosc. Univ. Math. Bull. 61, No. 4, 14-18 (2006).

In the paper a condition for a polynomial is established which is sufficient for its being the Chebyshev polynomial of prescribed power on given compact. This condition allows to compute the Chebyshev polynomials on the compacts of special form. Besides, particular extremal polynomials are introduced associated with this condition and their asymptotic properties are studied.

Reviewer: E. Ya. Smirnov (St. Petersburg)

MSC:

41A50

Best approximation, Chebyshev systems

Keywords:

given compact; Chebyshev polynomial

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