Bernstein n-Widths for Classes of Convolution Functions with Kernels Satisfying Certain Oscillation Properties  

作　　者：Guo FENG Gen Sun FANG 

机构地区：[1]School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, P. R. China [2]School of Mathematics and Information Engineering, Taizhou University, Taizhou 317000, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2009年第3期393-402,共10页数学学报（英文版）

基　　金：supported by the Natural Science Foundation of China (Grant No. 10671019);Research Fund for the Doctoral Program Higher Education (No. 20050027007);Scientific Research Fund of Zhejiang Provincial Education Department (No. 20070509)

摘　　要：In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.

关 键 词：Bernstein n-widths exact constants oscillation properties spectral of nonlinear integral equations 

分 类 号：O174.12[理学—数学]