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

DOI:
https://doi.org/10.1090/S0002-9947-06-03996-1

Published electronically:
June 13, 2006

MathSciNet review:
2231889

Full-text PDF Free Access

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 $\sum _{l\neq 0,l\in L}\frac {1}{l}=\infty$. 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

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