Integral inequalities for algebraic polynomials
نویسنده
چکیده
In this paper we consider two extremal problems for algebraic polynomials in L 2 metrics. (1) Let Pn be the class of all algebraic polynomials P(x) = akxk of degree at most nand IJPllda= (fIR IP(x)1 2 da(x))1/2, where da(x) is a nonnegative measure on lit We determine the best constant in the inequality lakl:::; Cn,k(da)IJPl!da-, for k = O,l, ... ,n, when P E Pn and such that = 0, k = 1, ... ,m. The cases Cn,n(da) and Cn,n-l(da) were studied by Milovanovic and Guessab [5], and only for the Legendre measure by Tariq
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