Journal of Applied Mathematics
Volume 2012 (2012), Article ID 495054, 9 pages
http://dx.doi.org/10.1155/2012/495054
Research Article

Bernstein Widths of Some Classes of Functions Defined by a Self-Adjoint Operator

Guo Feng

School of Mathematics and Information Engineering, Taizhou University, Taizhou 317000, China

Received 9 May 2011; Accepted 2 August 2011

Academic Editor: Kai Diethelm

Copyright © 2012 Guo Feng. 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 𝑊 𝑝 ( ℒ 𝑟 ) , which include the classical Sobolev class as its special case. Using the iterative method of Buslaev, with the help of the spectrum of linear differential equations, we determine the exact values of Bernstein width of the classes 𝑊 𝑝 ( ℒ 𝑟 ) in the space 𝐿 𝑞 for 1 < 𝑝 ≤ 𝑞 < ∞ .