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 Correspondence should be addressed to Guo Feng, [email protected] Received 9 May 2011; Accepted 2 August 2011 Academic Editor: Kai Diethelm Copyright q 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. 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. 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 Wp Lr in the space Lq for 1 < p ≤ q < ∞.