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

 

Inverse scattering with fixed energy and an inverse eigenvalue problem on the half-line


Author: Miklós Horváth
Journal: Trans. Amer. Math. Soc. 358 (2006), 5161-5177
MSC (2000): Primary 34A55, 34B20; Secondary 34L40, 47A75
Published electronically: June 13, 2006
MathSciNet review: 2231889
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Abstract | References | Similar Articles | Additional Information

Abstract: Recently A. G. Ramm (1999) has shown that a subset of phase shifts $ \delta_l$, $ l=0,1,\ldots$, determines the potential if the indices of the known shifts satisfy the Müntz condition $ \sum_{l\neq0,l\in L}\frac{1}{l}=\infty$. We prove the necessity of this condition in some classes of potentials. The problem is reduced to an inverse eigenvalue problem for the half-line Schrödinger operators.


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Additional Information

Miklós Horváth
Affiliation: Department for Mathematical Analysis, Institute of Mathematics, Technical University of Budapest, H 1111 Budapest, Műegyetem rkp. 3-9, Hungary
Email: horvath@math.bme.hu

DOI: http://dx.doi.org/10.1090/S0002-9947-06-03996-1
PII: S 0002-9947(06)03996-1
Keywords: Inverse scattering, inverse eigenvalue problem, $m$-function, completeness of exponential systems
Received by editor(s): April 2, 2003
Received by editor(s) in revised form: December 21, 2004
Published electronically: June 13, 2006
Additional Notes: This research was supported by Hungarian NSF Grants OTKA T 32374 and T 37491.
Article copyright: © Copyright 2006 American Mathematical Society