Dependence Rate of Equiconvergence on the Module of Continuity of Potential of the Sturm-Liouville Operator

Abstract

In this paper we consider the problem of local uniform equiconvergence with trigonometric series of orthogonal expansions in a system of eigenfunctions of the Sturm-Liouville operator with real potential q(x) is an element of L-1 (0, 1), for the function f (x) from the classes W-1(1) (0, 1) and W-r(1) (0, 1) (r greater than or equal to 1), f (0) = f (1) = 0. Rate of equiconvergence on every compact subset of (0, 1) is established. Rate of equiconvergence depends on the module of continuity of potential.