Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm-Liouville Operators

Schmidt, Karl Michael ORCID: https://orcid.org/0000-0002-0227-3024 2000. Critical Coupling Constants and Eigenvalue Asymptotics of Perturbed Periodic Sturm-Liouville Operators. Communications in Mathematical Physics 211 (2) , pp. 465-485. 10.1007/s002200050822

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Abstract

Perturbations of asymptotic decay c/r 2 arise in the partial-wave analysis of rotationally symmetric partial differential operators. We show that for each end-point λ0 of the spectral bands of a perturbed periodic Sturm–Liouville operator, there is a critical coupling constant c crit such that eigenvalues in the spectral gap accumulate at λ0 if and only if c/c crit>1. The oscillation theoretic method used in the proof also yields the asymptotic distribution of the eigenvalues near λ0.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Springer
ISSN:	0010-3616
Last Modified:	18 Oct 2022 13:25
URI:	https://orca.cardiff.ac.uk/id/eprint/13819

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