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一类三角级数的最佳逼近度“双边”单调性条件的重要应用 被引量：2

The Best Approximation Rate of Certain Trigonometric Series Important Applications of a "Two-sided" Monotonicity Condition
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摘要 在本质性推广了O-正则变化拟单调性的一个新条件下,本文在一般复值连续函数空间给出了一类三角级数最佳逼近度的完整结果,并建立了一个重要应用． The main object of the present paper is to give a complete result regarding the best approximation rate of certain trigonometric series in general complex valued continuous function space under a new condition which gives an essential generalization to O-regularly varying quasimonotonicity, An application is presented.
作者 周颂平 乐瑞君
机构地区 浙江理工大学数学研究所 宁波大学数学系
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2006年第3期509-518,共10页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金项目(10471130)
关键词 一致收敛 最佳逼近 拟单调 uniform convergence best approximation quasimonotone
分类号 O174.21 [理学—基础数学]
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参考文献11

  • 1Nurcombe J.R.,On the uniform convergence of sine series with quasimonotone coefficients,J.Math.Anal.Appl.,1992,166:577-581.
  • 2Xie T.F.and Zhou S.P.,The uniform convergence of certain trigonometric series,J.Math.Anal.Appl.,1994,181:171-180.
  • 3Stanojevic V.B.,L^1-convergence of Fourier series with complex quasimonotone coefficients,Proc.Amer.Math.Soc.,1982,86:241-247.
  • 4Stanojevic V.B.,L^1-con vergence of Fourier series with O-regularly varying quasimonotone coefficients,J.Approx.Theory,1990,60:168-173.
  • 5Xie T.F.and Zhou S.P.,L^1-approximation of Fourier series of complex valued functions,Proc.Royal Soc.Edinburgh,1996,126A:343-353.
  • 6Belov A.S.,On sequential estimate of best approximations and moduli of continuity by sums of trigonometric series with quasimonotone coefficients,Matem.Zametki,1992,51(4):132-134 (in Russian).
  • 7Xiao W.,Xie T.F.,Zhou S.P.,The best approximation rate of certain trigonometric series,Chinese Ann.Math.,2000,21A:81-88 (in Chinese).
  • 8Leindler L.,On the uniform convergence and boundedness of a certain class of sine series,Anal.Math.,2001,27:279-285.
  • 9Zhou S.P.and Le R.J.,A new condition for the uniform convergence of certain trigonometric series,Acta Math.Hungar.,2005,108:161-169.
  • 10Zhou S.P.,What strong monotonicity condition on Fourier coefficients can make the ratio ‖f-Sn(f)‖/En(f)bounded? Proc.Amer.Math.Soc.,1994,121:779-785.

同被引文献16

  • 1YU DanSheng1,2, ZHOU Ping2 & ZHOU SongPing1 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.On the relations among best approximation and Fourier coeffcients[J].Science China Mathematics,2008,51(10):1883-1894. 被引量：1
  • 2Ruijun Le,Songping Zhou.A NEW CONDITION FOR CERTAIN TRIGONOMETRIC SERIES[J].Analysis in Theory and Applications,2006,22(1):1-7. 被引量：2
  • 3周颂平.一类三角级数一致收敛性的一个注记(英文)[J].数学进展,2007,36(2):239-244. 被引量：7
  • 4Belov A S. On sequential estimate of best approximation and moduli of continuity by sums of trigonometric series with quasimonotone coefficients (in Russian). Matem Zemetki, 51:132-134 (1992)
  • 5Le R J, Zhou S P. A new condition for the uniform convergence of certain trigonometric series. Acta Math Hung, 108:161-169 (2005)
  • 6Leindler L. On the uniform convergence and boundedness of a certain class of sine series. Anal Math, 27: 279-285 (2001)
  • 7Yu D S, Zhou S P. A generalization of monotone condition and applications. Acta Math Hung, 115: 247-267 (2007)
  • 8Zhou S P. What strong monotonicity condition on Fourier coefficients can make the ratio ||f-Sn(f)||/En (f) bounded? Proc Amer Math Soc, 121:779-785 (1994)
  • 9Zhou S P, Zhou P, Yu D S. The ultimate condition to generalize monotonicity for uniform convergence of trigonometric series, arXiv: math.CA/0611805 v1, November 27, 2006, preprint
  • 10Zygmund A. Trigonometric Series, Vol Ⅰ, 2nd ed. Cambridge: Cambridge University Press, 1959

引证文献2

二级引证文献4

数学学报（中文版）
2006年 第3期

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