Volume 25, pp. 467-479, 2006.
On convergence of orthonormal expansions for exponential weights
H. P. Mashele
Abstract
Let be a real interval, finite or infinite, and let . Assume that is a weight,
so that we may define orthonormal polynomials corresponding to . For , let denote the th
partial sum of the orthonormal expansion of with respect to these
polynomials. We show that if , then as . The class of weights considered includes even
exponential weights.
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Key words
orthonormal polynomials, de la Vallée Poussin means
AMS subject classifications
65N12, 65F35, 65J20, 65N55