Oscillatory behavior of orthogonal polynomials

Máté, Attila; Nevai, Paul; Totik, Vilmos

doi:10.1090/S0002-9939-1986-0818456-1

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 is also described that is a pointwise bound for ${p_n}$ , exceeded only on sets of small measure. It is shown that is the best possible.

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