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In this paper we establish criteria for the existence and uniqueness of contractive solutions K of the Riccati equation KBK+KA&DK&C=0 under the assumption that the spectra of A and D are disjoint. Academic Press

We consider the regular Sturm Liouville problem y"& py+(*+qÂ(u&*)) y=0, which contains the eigenvalue parameter rationally. Under certain assumptions on p, q, and u it is shown that the spectrum of the problem consists of a continuous component (the range of the function u), discrete 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 Fourier transform are given. Academic Press

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