Journal of Inequalities and Applications 
Volume 2008 (2008), Article ID 894529, 8 pages
doi:10.1155/2008/894529
Research Article

Exact Values of Bernstein n-Widths for Some Classes of Periodic Functions with Formal Self-Adjoint Linear Differential Operators

Feng Guo

 Department of Mathematics, Taizhou University, Zhejiang, Taizhou 317000, China
Received 10 December 2007; Accepted 18 June 2008

Recommended by Vijay Gupta

Abstract

We consider the classes of periodic functions with formal self-adjoint linear differential operators Wp(ℒr), which include the classical Sobolev class as its special case. With the help of the spectral of linear differential equations, we find the exact values of Bernstein n-width of the classes Wp(ℒr) in the Lp for 1<p<∞.