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Orthogonal Polynomials and Christoffel Functions for Exp (−|X|a), a ≤ 1

✍ Scribed by A.L. Levin; D.S. Lubinsky

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 765 KB
Volume: 80
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1016

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✦ Synopsis

Let (W_{x}(x):=\exp \left(-|x|^{x}\right), x \in \mathbb{R}, x>0). For (\alpha \leqslant 1), we obtain upper and lower bounds for the Christoffel functions for the weight (W_{x}^{2}) over the whole MhaskarRahmanov-Saff interval, and deduce inequalities for spacing of zeros of orthogonal polynomials for (W_{x}^{2}). Then we deduce bounds for orthogonal polynomials for the weight (\boldsymbol{W}{x}^{2}). These results complement recent results of the authors treating a large class of weights including (W{x}^{2}, x>1). 1995 Academic Press, Inc.

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