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Christoffel Functions and Fourier Series for Multivariate Orthogonal Polynomials

✍ Scribed by Y. Xu

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 944 KB
Volume: 82
Category: Article
ISSN: 0021-9045
DOI: 10.1006/jath.1995.1075

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✦ Synopsis

The Christoffel functions (A_{n}(d \mu)) associated with a general nonnegative measure (\mu) on (\mathbb{R}^{d}) are studied. The asymptotics of (A_{n}(d \mu)) are derived for (\mu) supported on ([-1,1]^{d}). The estimates of (A_{n}(d \mu)) are used to study the summability of the multivariate orthogonal polynomials associated with (\mu). The pointwise convergence of the partial sums of the orthogonal expansion. and their ((C, 1)) and de la Vallée Poussin means are considered. is 1495 Academic Press, Inc

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