Abstract
In this chapter, we establish asymptotics of the extremal errors
where the inf is taken over all monic polynomials P of degree n. In order to state our result in compact form, we need some notation. For a non-negative h : [−1,1] → ℝ, let
denote the geometric mean of h. Recall also that
where L n is the linear map of [a −n, an] onto [−1,1] and L [−1]n is its inverse. Finally, let
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© 2001 Springer Science+Business Media New York
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Levin, E., Lubinsky, D.S. (2001). Asymptotics of Extremal Errors. In: Orthogonal Polynomials for Exponential Weights. CMS Books in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0201-8_8
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DOI: https://doi.org/10.1007/978-1-4613-0201-8_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6563-4
Online ISBN: 978-1-4613-0201-8
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