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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Oscillatory behavior of orthogonal polynomials
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by Attila Máté, Paul Nevai and Vilmos Totik PDF
Proc. Amer. Math. Soc. 96 (1986), 261-268 Request permission

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.
References
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Additional Information
  • © Copyright 1986 American Mathematical Society
  • 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