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

## 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.

Item type: | Article |
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ID code: | 4550 |

Keywords: | nonlinear eigenvalue problem, spectral density, block operator matrix, numerical mathematics, differential equations, Mathematics, Analysis |

Subjects: | Science > Mathematics |

Department: | Faculty of Science > Mathematics and Statistics |

Depositing user: | Strathprints Administrator |

Date Deposited: | 01 Nov 2007 |

Last modified: | 04 Sep 2014 13:15 |

URI: | http://strathprints.strath.ac.uk/id/eprint/4550 |

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