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On the relations among best approximation and Fourier coefficients

Authors:	DanSheng Yu Ping Zhou and SongPing Zhou

Institution:	(1) Institute of Mathematics, Zhejiang Sci-Tech University, Hangzhou, 310018, China;(2) Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Nova Scotia, Canada, B2G 2W5

Abstract:	We discuss the relations among the best approximation E _n(f) and the Fourier coefficients of a function, $\hat f(n) \in C,n = 0, \pm 1, \pm 2, \ldots ,$ under the conditions that $\{ \hat f(n)\} _{n = 0}^\infty \in MVBVS^$ and $\{ \hat f(n) + f( - n)\} _{n = 0}^\infty \in MVBVS^$ , where MVBVS^* is the class of the so-called Strong Mean Value Bounded Variation Sequences. This work was supported by NSERC RCD grant and AARMS of Canada (Yu D S), by NSERC of Canada (Zhou P), and by the National Natural Science Foundation of China (Grant No. 10471130) and the Open Fund (Grant No. PLN0613) of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation (Southwest Petroleum University) (Zhou S P)

Keywords:	best approximation Fourier coefficients mean value bounded variation
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