Transactions of the American Mathematical Society

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

Author(s): F. Gesztesy; B. Simon
Journal: Trans. Amer. Math. Soc. 348 (1996), 349-373.
MSC (1991): Primary 34B24, 34L05, 81Q10; Secondary 34B20, 47A10
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 34B24, 34L05, 81Q10, 34B20, 47A10

F. Gesztesy
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: mathfg@mizzou1.missouri.edu

B. Simon
Affiliation: Division of Physics, Mathematics, and Astronomy, California Institute of Technology, 253-37, Pasadena, California 91125

DOI: 10.1090/S0002-9947-96-01525-5
PII: S 0002-9947(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.
Copyright of article: Copyright 1996, by the authors

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