Inverse scattering with fixed energy and an inverse eigenvalue problem on the half-line
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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.References
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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
- 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.
- © Copyright 2006 American Mathematical Society
- 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
- MathSciNet review: 2231889