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Geometric aspects of self-adjoint Sturm–Liouville problems
Published online by Cambridge University Press: 14 August 2017
Extract
In this paper we use U(2), the group of 2 × 2 unitary matrices, to parametrize the space of all self-adjoint boundary conditions for a fixed Sturm–Liouville equation on the interval [0, 1]. The adjoint action of U(2) on itself naturally leads to a refined classification of self-adjoint boundary conditions – each adjoint orbit is a subclass of these boundary conditions. We give explicit parametrizations of those adjoint orbits of principal type, i.e. orbits diffeomorphic to the 2-sphere S2, and investigate the behaviour of the nth eigenvalue λnas a function on such orbits.
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 6 , December 2017 , pp. 1279 - 1295
- Copyright
- Copyright © Royal Society of Edinburgh 2017