NECESSARY AND SUFFICIENT CONDITIONS FOR MEAN CONVERGENCE OF ORTHOGONAL EXPANSIONS FOR FREUD WEIGHTS

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/28028

Title:	NECESSARY AND SUFFICIENT CONDITIONS FOR MEAN CONVERGENCE OF ORTHOGONAL EXPANSIONS FOR FREUD WEIGHTS
Authors:	JHA,SW;LUBINSKY,DS
Contributors:	數學研究所
Keywords:	EXPONENTIAL WEIGHTS;CHRISTOFFEL FUNCTIONS;POLYNOMIAL LIVE;LAGUERRE SERIES;HERMITE;BOUNDS;INEQUALITIES;NORM
Date:	1995
Issue Date:	2010-06-29 19:40:34 (UTC+8)
Publisher:	中央大學
Abstract:	A classic 1970 paper of B. Muckenhoupt established necessary and sufficient conditions for weighted L(p) convergence of Hermite series, that is, orthogonal expansions corresponding to the Hermite weight. We generalize these to orthogonal expansions for a class of Freud weights W-2 := e(-2Q), by first proving a bound for the difference of the orthonormal polynomials of degree n + 1 and n - 1 of the weight W-2. Our identical necessary and sufficient conditions close a slight gap in Muckenhoupt's conditions for the Hermite weight at least for p > 1. Moreover, our necessary conditions apply when Q(x) = \x\(alpha), alpha > 1, while our sufficient conditions apply at least for alpha = 2, 4, 6,....
Relation:	CONSTRUCTIVE APPROXIMATION
Appears in Collections:	[Graduate Institute of Mathematics] journal & Dissertation

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