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

Adamjan, V. and Langer, Heinz and Langer, M. (2001) A spectral theory for a λ-rational Sturm-Liouville problem. Journal of Differential Equations, 171 (2). pp. 315-345. ISSN 0022-0396 (https://doi.org/10.1006/jdeq.2000.3841)

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Abstract

We consider the regular Sturm-Liouville problem y″−py+(λ+q/(u−λ)) 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.

ORCID iDs

Adamjan, V., Langer, Heinz and Langer, M. ORCID logoORCID: https://orcid.org/0000-0001-8813-7914;
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