Discreteness of some continuous spectrum eigenfunction expansions

Hinton, Don B.; Kauffman, Robert M.

doi:10.1090/S0002-9939-1993-1174493-5

Discreteness of some continuous spectrum eigenfunction expansions
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by Don B. Hinton and Robert M. Kauffman

Proc. Amer. Math. Soc. 119 (1993), 235-243

DOI: https://doi.org/10.1090/S0002-9939-1993-1174493-5

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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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