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Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators


Authors: F. Gesztesy and B. Simon
Journal: Trans. Amer. Math. Soc. 348 (1996), 349-373
MSC (1991): Primary 34B24, 34L05, 81Q10; Secondary 34B20, 47A10
DOI: https://doi.org/10.1090/S0002-9947-96-01525-5
MathSciNet review: 1329533
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Abstract: New unique characterization results for the potential $V(x)$ in connection with Schrödinger operators on $\mathbb{R}$ and on the half-line $[0,\infty )$ are proven in terms of appropriate Krein spectral shift functions. Particular results obtained include a generalization of a well-known uniqueness theorem of Borg and Marchenko for Schrödinger operators on the half-line with purely discrete spectra to arbitrary spectral types and a new uniqueness result for Schrödinger operators with confining potentials on the entire real line.


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Additional Information

F. Gesztesy
Email: mathfg@mizzou1.missouri.edu

DOI: https://doi.org/10.1090/S0002-9947-96-01525-5
Keywords: Schrdinger operators, inverse spectral theory, Krein's spectral shift function
Received by editor(s): February 27, 1995
Additional Notes: This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The U.S. Government has certain rights in this material.
Article copyright: © Copyright 1996 by the authors