The Expansion Problem with Boundary Conditions at a Finite Set of Points

Abstract

The problem of expanding an arbitrary function in a series of characteristic solutions of the ordinary differential equation(1.1)and the boundary relations(1.2)is well known. The various discussions are distinguished by the manner in which a parameter λ appears in the differential system and by the number of points at which the boundary conditions apply. The case in which the boundary conditions apply at intermediate as well as at the end points of a fundamental interval has been considered by Wilder (3).