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Transactions of the American Mathematical Society

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Inverse spectral analysis with partial information on the potential, II. The case of discrete spectrum

Authors: Fritz Gesztesy and Barry Simon
Journal: Trans. Amer. Math. Soc. 352 (2000), 2765-2787
MSC (2000): Primary 34A55, 34L40; Secondary 34B20
Published electronically: December 10, 1999
MathSciNet review: 1694291
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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.

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Additional Information

Fritz Gesztesy
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211

Barry Simon
Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology, Pasadena, California 91125

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.
Article copyright: © Copyright 2000 by the Authors