On the pointwise convergence of the eigenfunction expansion associated with some iterated boundary value problems

Abstract

Given a boundary value problem consisting of a second-order differential equation and some boundary conditions, one can derive higher-order boundary value problems, called iterated boundary value problems, provided the coefficients in the second-order differential equation are sufficiently smooth. The problem of convergence of the eigenfunction expansions associated with boundary value problems of even order has been the central attraction for mathematicians since the beginning of this century. The idea of this paper is to single out some higher-order boundary value problems, for which the question of convergence of the said expansion is completely answered by the similar problem associated with the second-order boundary value problem responsible for the generation of the iterated boundary value problem.