Markov-Type Inequalities for Products of Müntz Polynomials Revisited | Chapter individual record

© Springer International Publishing AG 2017. Professor Rahman was a great expert of Markov-and Bernstein-type inequalities for various classes of functions, in particular for polynomials under various constraints on their zeros, coefficients, and so on. His books are great sources of such inequalities and related matters. Here we do not even try to survey Rahman’s contributions to Markov-and Bernstein-type inequalities and related results. We focus on Markov-type inequalities for products of Müntz polynomials. Let Λn: {λ0 < λ1 <···< λn} be a set of real numbers.We denote the linear span of xλ0, xλ1,∙∙∙xλn over R by M(Λn):= span{xλ0, xλ1,∙∙∙xλn}. Elements of M(Λn) are called Müntz polynomials. The principal result of this paper is a Markov-type inequality for products of Müntz polynomials on intervals [a, b] ⊂ (0, ∞) which extends a less general result proved in an earlier publication. It allows us to answer some questions asked by Thomas Bloom recently in e-mail communications. The author believes that the new results in this paper are sufficiently interesting and original to serve as a tribute to the memory of Professor Rahman in this volume.

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Erdélyi, T.
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