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
Department of Mathematics, Taizhou University, Zhejiang, Taizhou 317000, China
Received 10 December 2007; Accepted 18 June 2008
Academic Editor: Vijay Gupta
Copyright © 2008 Feng Guo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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<∞.