a1 Department of Mathematics, The Pennsylvania State University
In this paper it is shown that the analysis of Titchmarsh's book  for regular Sturm-Liouville problems on a finite closed interval carries over readily to regular problems involving the eigenvalue parameter in the boundary condition at one end-point. The manner in which this type of problem is associated with a self-adjoint operator in Hilbert space has recently been pointed out by Walter in , and his operator-theoretic formulation is adopted here. The use of the eigenfunction expansion is illustrated by applying it to solve a heat-conduction problem for a solid in contact with a fluid.
(Received February 02 1976)