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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 spectral analysis with partial information on the potential, II. The case of discrete spectrum
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by Fritz Gesztesy and Barry Simon PDF
Trans. Amer. Math. Soc. 352 (2000), 2765-2787

Abstract:

We discuss results where the discrete spectrum (or partial information on the discrete spectrum) and partial information on the potential $q$ of a one-dimensional Schrödinger operator $H=-\frac {d^{2}}{dx^{2}}+q$ determine the potential completely. Included are theorems for finite intervals and for the whole line. In particular, we pose and solve a new type of inverse spectral problem involving fractions of the eigenvalues of $H$ on a finite interval and knowledge of $q$ over a corresponding fraction of the interval. The methods employed rest on Weyl $m$-function techniques and densities of zeros of a class of entire functions.
References
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Additional Information
  • Fritz Gesztesy
  • Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
  • MR Author ID: 72880
  • Email: fritz@math.missouri.edu
  • Barry Simon
  • Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125
  • MR Author ID: 189013
  • Email: bsimon@caltech.edu
  • Received by editor(s): October 9, 1997
  • Published electronically: December 10, 1999
  • Additional Notes: This material is based upon work supported by the National Science Foundation under Grant Nos. DMS-9623121 and DMS-9401491.
  • © Copyright 2000 by the Authors
  • Journal: Trans. Amer. Math. Soc. 352 (2000), 2765-2787
  • MSC (2000): Primary 34A55, 34L40; Secondary 34B20
  • DOI: https://doi.org/10.1090/S0002-9947-99-02544-1
  • MathSciNet review: 1694291