Db. Hinton et Rm. Kauffman, DISCRETENESS OF SOME CONTINUOUS-SPECTRUM EIGENFUNCTION-EXPANSIONS, Proceedings of the American Mathematical Society, 119(1), 1993, pp. 235-243
We discuss replacing the integrals in continuous spectrum expansions b
y finite sums, in the special case of the Dirichlet problem for second
-order ordinary differential operators on a half-line. The error is co
ntrolled in the operator norm of B(Y, Z), where Y and Z are natural Hi
lbert spaces for the problem.