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Inverse spectral theory for Sturm-Liouville problems with finite spectrum

Authors: Hans Volkmer and Anton Zettl
Journal: Proc. Amer. Math. Soc. 135 (2007), 1129-1132
MSC (2000): Primary 34B24, 34B09; Secondary 34L05
Published electronically: October 11, 2006
MathSciNet review: 2262915
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Abstract | References | Similar Articles | Additional Information

Abstract: For any positive integer $ n$ and any given $ n$ distinct real numbers we construct a Sturm-Liouville problem whose spectrum is precisely the given set of $ n$ numbers. Such problems are of Atkinson type in the sense that the weight function or the reciprocal of the leading coefficient is identically zero on at least one subinterval.

References [Enhancements On Off] (What's this?)

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  • 2. P. Binding and H. Volkmer, ``Prüfer angle asymptotics for Atkinson's semi-definite Sturm-Liouville eigenvalue problem'', to appear in Math. Nachr.
  • 3. F. P. Gantmacher and M. G. Krein, ``Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems'', Amer. Math. Soc. Chelsea Publishing, Providence, Rhode Island, (2002). MR 1908601 (2003f:34161)
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Additional Information

Hans Volkmer
Affiliation: Department of Mathematical Sciences, University of Wisconsin, Milwaukee, Wisconsin 53201

Anton Zettl
Affiliation: Department of Mathematics, Northern Illinois University, De Kalb, Illinois 60115

Keywords: Sturm-Liouville problems, finite spectrum, inverse spectral theory
Received by editor(s): March 21, 2005
Received by editor(s) in revised form: November 11, 2005
Published electronically: October 11, 2006
Dedicated: Dedicated to the memory of F.V. Atkinson
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2006 American Mathematical Society

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