Pointwise convergence of eigenfunction expansions, associated with a pair of ordinary differential expressions

Abstract

SynopsisFor the differential equation Lf = λMf on an open interval of ℝ, a theory in terms of relations in a Hilbert space associated with M was developed in a paper by Coddington and de Snoo, and eigenfunction expansions were derived in a paper by Dijksma and de Snoo. In the case of a regular problem on a compact interval, pointwise convergence of the expansions was shown in another paper by Coddington and de Snoo. Here, we show pointwise convergence in the general singular case.