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Isospectral sets for boundary value problems on the unit interval

Published online by Cambridge University Press:  10 December 2009

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Abstract

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We analyse isospectral sets of potentials associated to a given ‘generalized periodic’ boundary condition in SL(2, R) for the Sturm-Liouville equation on the unit interval. This is done by first studying the larger manifold M of all pairs of boundary conditions and potentials with a given spectrum and characterizing the critical points of the map from M to the trace a + d Isospectral sets appear as slices of M whose geometry is determined by the critical point structure of the trace function. This paper completes the classification of isospectral sets for all real self-adjoint boundary conditions.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 8 , Volume 8: Charles Conley Memorial Issue , December 1988 , pp. 301 - 358
Copyright
Copyright © Cambridge University Press 1988

Footnotes

†

With an appendix by Johan Tysk, Department of Mathematics, University of California, Los Angeles, CA 90024, USA.

References

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