EQUICONVERGENCE THEOREMS FOR STURM^LIOVILLE OPERATORS WITH SINGULAR POTENTIALS (RATE OF EQUICONVERGENCE IN W|-NORM)

Abstract

We studv the Sturm-Liouville operator Ly = l(y) = + q(x)y with ax2 Diriehlet boundary conditions y(0) = y(n) = 0 in the space L2[0,n], We assume that the potential has the form q(x) = u'(x), where u G W|[0,n] with 0 < в < 1/2. Here W|[0,n] = [L2,W2,]e is the Sobolev space. We consider the problem of equieonvergenee in W|[0, n]-norm of two expansions of a function f G L2[0,n], The first one is constructed using the system of the eigenfunctions and associated