Markov-type inequalities for products of Muntz polynomials
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Let : = (j)j=0 be a sequence of distinct real numbers. The span of {x0, x1, , xn} over is denoted by Mn():=span{x0, x1, , xn}. Elements of Mn(a) are called Mntz polynomials. The principal result of this paper is the following Markov-type inequality for products of Mntz polynomials. Theorem 2.1. Let :=(j)j=0 and :=(j)j=0 be increasing sequences of nonnegative real numbers. Let In particular, 2/3(n+1) n K(Mn(), Mn()) 36(2n+1) n. Under some necessary extra assumptions, an analog of the above Markov-type inequality is extended to the cases when the factor x is dropped, and when the interval [0, 1] is replaced by [a, b] (0, ). 2001 Academic Press.