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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Inverse scattering with fixed energy and an inverse eigenvalue problem on the half-line
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by Miklós Horváth PDF
Trans. Amer. Math. Soc. 358 (2006), 5161-5177 Request permission

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
  • 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