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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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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Additional Information

Hans Volkmer
Affiliation: Department of Mathematical Sciences, University of Wisconsin, Milwaukee, Wisconsin 53201
Email: volkmer@csd.uwm.edu

Anton Zettl
Affiliation: Department of Mathematics, Northern Illinois University, De Kalb, Illinois 60115
Email: zettl@math.niu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08563-7
PII: S 0002-9939(06)08563-7
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