A spectral theory for a lambda-rational Sturm-Liouville problem

We consider the regular Sturm Liouville problem y" - py + (lambda + q/(u - lambda)) y = 0, which contains the eigenvalue parameter rationally. Under c ertain assumptions on p. q. and rr it is shown that the spectrum of the pro blem consists of a continuous component (thr range of the function u ). dis crete eigenvalues. and possibly a finite number of embedded eigenvalues. In the considered situation the continuous spectrum is absolutely continuous, and explicit formulas for the spectral density and the corresponding Fouri er transform are given. (C) 2001 Academic Press.