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A class of functions having the same best approximation for all Lp norms (1≦P≦∞)

Authors:	Shi Yingguang

Institution:	(1) Chinese Academy of Sciences, China

Abstract:	This paper gives a class of functions having the excellent property that L_{p, n} f=S_nf for all n and all p,1≤p≤∞, L_{p, n}f and S_nf being the best approximations to f in the L_p norm with weight w_p and the partial sum of the orthogonal expansion of f, respectively. Supported by National Naturol Science Fundation of China

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