Dependence rate of equiconvergence on the module of continuity of potential of the Sturm-Liouville operator

Kurbanov V.

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, vol.41, no.3, pp.347-364, 2004 (SCI-Expanded) identifier identifier


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.