Equiconvergence Rate in Terms of General Moduli of Continuity for Differential Operators

Abstract

In this paper the ordinary nonselfadjoint differential operator L, defined by a differential expression with nonzero nonsmooth coefficient of the (n− l)-th derivative and two-point Birkhoff-regular boundary conditions, is considered. The problem of uniform equicon-vergence of the expansion of a given function in series in terms of the eigenfunctions and associated functions of L and in terms of the trigonometric system is investigated. Estimates of the equiconvergence rate in terms of moduli of continuity of the expanded function and the coefficient of the (n − l)-th derivative are obtained.