Gesztesy, F. and Simon, B. (1996) Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators. Transactions of the American Mathematical Society, 348 (1). pp. 349-373. ISSN 0002-9947 http://resolver.caltech.edu/CaltechAUTHORS:20120208-090710174
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New unique characterization results for the potential V(x) in connection with Schrödinger operators on R and on the half-line [0,∞)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.
|Additional Information:||© 1996 by the authors. Received by the editors February 27, 1995. 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.|
|Subject Keywords:||Schrödinger operators, inverse spectral theory, Krein's spectral shift function.|
|Classification Code:||MSC 1991: Primary 34B24, 34L05, 81Q10; Secondary 34B20, 47A10.|
|Official Citation:||Uniqueness theorems in inverse spectral theory for one-dimensional Schrödinger operators F. Gesztesy; B. Simon Trans. Amer. Math. Soc. 348 (1996), 349-373.|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||08 Feb 2012 17:33|
|Last Modified:||26 Dec 2012 14:48|
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