某些周期函数类的Bernstein n -宽度的极子空间

Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (2): 292-297.

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Optimal Subspace of Bernstein n-Widths for Some Classes of Periodic Functions

FENG Guo

School of Mathematics and Information Engineering, Taizhou University, Zhejiang Taizhou 317000, School of Mathematical Sciences, |Beijing Normal University, |Beijing 100875

Received:2011-03-18 Revised:2012-11-12 Online:2013-04-25 Published:2013-04-25
Supported by:
国家自然科学基金(10671019)、浙江省自然科学基金(LY12A01008)和台州学院培育基金资助

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Abstract

Abstract:

In this paper, we consider Bernstein n-width of the classes of 2π-periodic convolution functions K_p and B_p, obtain their optimal subspaces in L^p for n odd and p∈(1, ∞).

Key words: NCVD-kernel, B-kernel, Bernstein n-widths, Optimal subspace

CLC Number:

41A10

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FENG Guo. Optimal Subspace of Bernstein n-Widths for Some Classes of Periodic Functions[J].Acta mathematica scientia,Series A, 2013, 33(2): 292-297.

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References

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[2] Feng Guo, Fang Gensun. Bernstein n-widths for classes of convolution functions with kernels satisfying certain oscillation properties. Acta Mathematica Sinica (English Series), 2009, 25(3): 394--402

[3] Lorentz G G, Golitschek M V, Makovoz Y. Constructive Approximation Advanced Problems. Berlin, Heidelberg: Springer-Verlag, 1996

[4] Magaril-IL'yaev G G. Mean dimension, widths, and optimal recovery of sobolev classes of functions on the line. Math USSR Sbornik, 1993, 74(2): 381--403

[5] Pinkus A. n-Widths in Approximation Theory. Berlin: Springer-Verlag, 1985

[6] Pinkus A. n-Widths of Sobolev spaces in L^p. Constr Approx, 1985, 1: 15--62

[7] Tikhomirov V M. Some Problems on Approximation Theory. Moscow (in Russian): Izd Mosk Univ, 1976

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