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一个二元周期函数类的正交投影宽度

Orthowidths of Some Class of Periodic Functions of Two Variables
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摘要 本文得到了二元周期可微函数类△_p^r在空间L_q(T^2)中的正交投影宽度d1/N(△_p^r,L_q)的渐近精确阶. The following asymptotic order of orthowidths d1/N(△^rp, Lq) of class of functions 1 in the metric Lq(T^2) is obtained for 1 〈p,q 〈 ∞ and r 〉 (1/p -1/q)+:d1/N(△^rp ,Lq)=N^-r+(1/p-1/q)+and the Fourier partial sum Snn (f) (n=√N) is an asymptotic optimal orthogonal projection operator.
作者 罗俊波
出处 《数学进展》 CSCD 北大核心 2006年第5期629-634,共6页 Advances in Mathematics(China)
关键词 正交投影宽度 函数类△^rp Fourier部分和 orthowidths class of functions △^rp Fourier partial sum
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参考文献6

  • 1Temlyakov,V.N.,Widths of some classes of functions of several variables,Dokl.Akad.Nauk SSSR,1982,267(2):314-317.
  • 2Luo Junbo,On the width of class of periodic functions of two variables,in book:Approximation,Optimization and Computing,kdited by A.G.Law and C.L.Wang,North-Holland,1990,147-150.
  • 3Stein,E.M.and Weiss,G.,Introduction to Fourier Analysis on Euclidean Space,Princeton Univ.Press,1971.
  • 4Zygmund,A.,Trigonometric Series,Cambridge Univ.press,1965.
  • 5Galeev,E.M.,Orders of orthogonal projection widths of classes of periodic functions of one and several variables,Math.Zametki,1988,43(2):197-211.
  • 6Sun Yongsheng,Approximation Theory,Vol.1,Beijing Normal Univ.Press,1989(in Chinese).

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