Resolvent Means and InvertingGeneralized Fourier Transforms

Raphael, Louise A.

Canadian journal of mathematics, Tome 38 (1986) no. 4, pp. 861-877

Résumé

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.

Détail

DOI : 10.4153/CJM-1986-042-7

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