Geometric aspects of self-adjoint Sturm–Liouville problems
2017 ◽
Vol 147
(6)
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pp. 1279-1295
Keyword(s):
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.
1988 ◽
Vol 8
(8)
◽
pp. 301-358
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2002 ◽
Vol 45
(3)
◽
pp. 631-645
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Keyword(s):
2017 ◽
2020 ◽
Vol 5
(1)
◽
pp. 361-368
1956 ◽
Vol 52
(4)
◽
pp. 636-639
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2003 ◽
Vol 55
(4)
◽
pp. 724-749
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