Original scientific paper

On weighted Turan type inequality

Wei Xiao
Songping Zhou

Abstract

Let Hn be the class of real algebraic polynomials of degree n, whose zeros all lie in the interval [-1, 1]. Define || f || = max-1 ≤ x ≤ 1 | f(x)|. In 1939, Turan proved that for f ∈ Hn, || f ' || ≥ C√n || f ||. Usually, to establish weighted inequalities for polynomials requires more complicated techniques, especially in general cases. The object of this paper is to start the work in uniform norm under general requirements for weight functions.

Keywords

Turan type inequality

Hrčak ID:

6413

URI

https://hrcak.srce.hr/6413

Publication date:

1.12.1999.

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