N-Widths and Average Widths of Besov Classes in Sobolev Spaces

N-Widths and Average Widths of Besov Classes in Sobolev Spaces

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摘要 In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively. In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.

作者 Gui Qiao XU Yong Sheng SUN Yong Ping LIU

机构地区 School of Mathematical Sciences School of Mathematical Sciences

出处《Acta Mathematica Sinica,English Series》 SCIE CSCD 2006年第6期1667-1678,共12页 数学学报（英文版）

基金 Supported by Project(No.10471010)of National Natural Science Foundation of China Supported by the Development Foundation of Science and Technology of Tianjin Universities(20040405) Supported by Project"Representation Theory and Related Topics"of the"985 Program"of Beijing Normal University

关键词 Besov class n-width Sobolev space Average width Besov class, n-width, Sobolev space, Average width

分类号 O177 [理学—基础数学]

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1Nikol'skii, S. M.: Approximation of Functions of Several Variables and Imbedding Theorems, Spring-Verlag,New York, 1975
2Pinkus, A.: N-widths in approximation theory, Springer-Verlag, New York, 1985
3Romanyuk, A. S.: Approximation for Besov-type classes of periodic functions in Lq space. Ukraine Mat.Zh., 43(10), 1398-1408 (1991)
4Romanyuk, A. S.: Optimal trigonometric approximation and Kolmogorov widths for Besov classes of multivariate functions. Ukraine Mat. Zh., 45(5), 663-675 (1993)
5Romanyuk, A. S.: Kolmogorov widths for classes B^rp,θ of multivariate periodic functions with small smoothness in the space Lq. Ukraine Mat. Zh., 46(7), 915-926 (1994)
6Pustovoitov, N. N.i Representation and approximation of multivariate periodic functions with a given modulus of smoothness. Analysis Math., 20, 35-48 (1994)
7Sun, Y. S., Wang, H. P.: Representation and approximation of multivariate functions with bounded mixed modulus of smoothness. Proceedings of the Steklov Institute of Mathematics, 219,350-371 (1997)
8Li, C.: Infinite dimensional widths of function classes, d. Approx. Theory, 69(1), 15-34 (1992)
9Margaril-II'yaev, G. G.: Average dimension, widths, and optimal recovery of Sobolev classes on the real axis. Math. Sbornik, 182(11), 1635-1656 (1991) (In Russian)
10Luo, J. B., Liu, Y. P.: Average width and optimal recovery of the anisotropic classes W^rH^a(R^d) in the metric C^k(R^d). Analysis Mathematica, 24, 265-273 (1998)

1蒋艳杰.Average widths of anisotropic Besov-Wiener classes[J].Science China Mathematics,2000,43(6):609-615.
2Yanjie Jiang,Yongping Liu.Average widths and optimal recovery of multivariate Besov classes in L_p(R^d)[J].Chinese Science Bulletin,1998,43(8):638-641. 被引量：4
3GuiQiaoXU YongPingLIU.The Average Widths of Sobolev-Wiener Classes and Besov-Wiener Classes[J].Acta Mathematica Sinica,English Series,2004,20(1):81-92.
4He Ping WANG Department of Mathematics, Capital Normal University. Beijing, 100037, P. R. China.Average Widths of Sobolev-Wiener Classes with Mixed Smoothness in L_q(R^d)[J].Acta Mathematica Sinica,English Series,2001,17(2):305-312.
5Yong-ping Liu, Gui-qiao XuDepartment of Mathematics, Beijing Normal University, Beijing 100875, China Department of Mathematics, Tianjin Normal Univesity, Tianjin 300074. China.The Average Widths and Non-linear Widths of the Classes of Multivariate Functions with Bounded Moduli of Smoothness[J].Acta Mathematicae Applicatae Sinica,2002,18(4):663-674. 被引量：2
6费义艳,王旭,吕惠宾,杨国桢,朱湘东.Unit-Cell by Unit-Cell Homoepitaxial Growth Using Atomically Flat SrTiO3（001） Substrates and Pulsed Laser Deposition[J].Chinese Physics Letters,2005,22(4):1002-1005.

Acta Mathematica Sinica,English Series

2006年第6期

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N-Widths and Average Widths of Besov Classes in Sobolev Spaces

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