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Discreteness of some continuous spectrum eigenfunction expansions

Authors: Don B. Hinton and Robert M. Kauffman
Journal: Proc. Amer. Math. Soc. 119 (1993), 235-243
MSC: Primary 34L10; Secondary 47A70, 47E05
MathSciNet review: 1174493
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Abstract: We discuss replacing the integrals in continuous spectrum expansions by finite sums, in the special case of the Dirichlet problem for second-order ordinary differential operators on a half-line. The error is controlled in the operator norm of $ B(Y,Z)$, where $ Y$ and $ Z$ are natural Hilbert spaces for the problem.

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Article copyright: © Copyright 1993 American Mathematical Society