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 0022-0396Full text not available in this repository. (Request a copy from the Strathclyde author)
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.
|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:||29 Apr 2016 07:56|