Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems

Brown, Brian Malcolm ORCID: https://orcid.org/0000-0002-2871-6591 and Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046 2001. Spectral inclusion and spectral exactness for singular non-self-adjoint Sturm-Liouville problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 457 (2005) , pp. 117-139. 10.1098/rspa.2000.0659

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Abstract

We consider the effect of regularization by interval truncation on the spectrum of a singular non‐self‐adjoint Sturm‐Liouville operator. We present results on spectral inclusion and spectral exactness for the cases where the singularity is in Sims case II or Sims case III. For Sims case I, we present a test for spectral inexactness, which can be used to detect when the interval truncation process is generating spurious eigenvalues. Numerical results illustrate the effectiveness of this test.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics Computer Science & Informatics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Uncontrolled Keywords:	Sturm-Liouville problem; eigenvalue problem; non–self–adjoint; spectral inclusion; spectral exactness; titchmarsh-weyl function
Publisher:	Royal Society
ISSN:	1364-5021
Last Modified:	18 Oct 2022 13:23
URI:	https://orca.cardiff.ac.uk/id/eprint/13716

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