Extensions of Schur’s Inequality for the Leading Coefficient of Bounded Polynomials with Two Prescribed Zeros

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 41)


We extend Schur’s Chebyshev-type inequality([18], p. 285) for the leading coefficient of polynomials that are uniformly bounded on the interval [ − 1, 1] and vanish at its endpoints. Our extension is threefold: We obtain sharp V.A. Markov-type estimates for all single coefficients as well as sharp Szegö-type estimates for consecutive pairs of coefficients of such polynomials, and both these estimates imply Schur’s inequality for the leading coefficient. Thirdly, we consider a larger class of admissible polynomials by replacing uniform with pointwise boundedness on [ − 1, 1].


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.HagenGermany

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