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Resolvent Means and InvertingGeneralized Fourier Transforms

Published online by Cambridge University Press:  20 November 2018

Louise A. Raphael
Louise A. Raphael*
Affiliation:
Howard University, Washington, D.C.
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Let S-L denote a singular Sturm-Liouville system on the half line with homogeneous boundary conditions, possessing a discrete negative and continuous positive spectrum. Let A be the S-L operator and Sα(f; x) the S-L eigenfunction expansion associated with the resolvent operator (z – A)–1, z complex. That is, Sα(f; x) denotes the resolvent summability means with weight function z(z – λ)–1 (or (1 + tλ)–1 where t = – 1/z).

We first study the problem of determining when

(1)

where is the Green's function associated with a certain perturbation of our system.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 4 , 01 August 1986 , pp. 861 - 877
Copyright
Copyright © Canadian Mathematical Society 1986

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