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Proceedings of the American Mathematical Society

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Oscillatory behavior of orthogonal polynomials


Authors: Attila Máté, Paul Nevai and Vilmos Totik
Journal: Proc. Amer. Math. Soc. 96 (1986), 261-268
MSC: Primary 42C05
DOI: https://doi.org/10.1090/S0002-9939-1986-0818456-1
MathSciNet review: 818456
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Abstract: Let $ d\alpha $ be a positive Borel measure in [-1,1] with $ \alpha ' > 0$ a.e. It is shown that the polynomials $ {p_n}$ orthonormal with respect to this measure oscillate almost everywhere in [-1,1]. A function $ F$ is also described that is a pointwise bound for $ {p_n}$, exceeded only on sets of small measure. It is shown that $ F$ is the best possible.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0818456-1
Keywords: Orthogonal polynomials, Szegö's theory, weak convergence, mean convergence
Article copyright: © Copyright 1986 American Mathematical Society