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

Abstract

We consider the classes of periodic functions with formal self-adjoint linear differential operators $W_p\left({ℒ}_r\right)$, 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 $W_p\left({ℒ}_r\right)$ in the space $L_q$ for .