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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the inverse spectral theory of Schrödinger and Dirac operators


Author: Miklós Horváth
Journal: Trans. Amer. Math. Soc. 353 (2001), 4155-4171
MSC (1991): Primary 34A55, 34B20; Secondary 34L40, 47A75
Published electronically: May 17, 2001
MathSciNet review: 1837225
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Abstract | References | Similar Articles | Additional Information

Abstract:

We prove that under some conditions finitely many partially known spectra and partial information on the potential entirely determine the potential. This extends former results of Hochstadt, Lieberman, Gesztesy, Simon and others.


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Additional Information

Miklós Horváth
Affiliation: Budapest University of Technology and Economics, Institute of Mathematics, H 1111 Budapest, Műegyetem rkp. 3-9, Hungary
Email: horvath@math.bme.hu

DOI: http://dx.doi.org/10.1090/S0002-9947-01-02765-9
PII: S 0002-9947(01)02765-9
Keywords: Inverse spectral theory, $m$-function, spectral function
Received by editor(s): February 16, 2000
Received by editor(s) in revised form: June 7, 2000
Published electronically: May 17, 2001
Additional Notes: Research supported by the Hungarian NSF Grant OTKA T#32374
Article copyright: © Copyright 2001 American Mathematical Society