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

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题名:	NECESSARY AND SUFFICIENT CONDITIONS FOR MEAN CONVERGENCE OF ORTHOGONAL EXPANSIONS FOR FREUD WEIGHTS
作者:	JHA,SW;LUBINSKY,DS
贡献者:	數學研究所
关键词:	EXPONENTIAL WEIGHTS;CHRISTOFFEL FUNCTIONS;POLYNOMIAL LIVE;LAGUERRE SERIES;HERMITE;BOUNDS;INEQUALITIES;NORM
日期:	1995
上传时间:	2010-06-29 19:40:34 (UTC+8)
出版者:	中央大學
摘要:	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,....
關聯:	CONSTRUCTIVE APPROXIMATION
显示于类别:	[數學研究所] 期刊論文

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