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. doi:10.1090/S0002-9947-96-01525-5. https://resolver.caltech.edu/CaltechAUTHORS:20120208-090710174
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Abstract
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.
| Item Type: | Article | |||||||||
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| 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. | |||||||||
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| Subject Keywords: | Schrödinger operators, inverse spectral theory, Krein's spectral shift function. | |||||||||
| Issue or Number: | 1 | |||||||||
| Classification Code: | MSC 1991: Primary 34B24, 34L05, 81Q10; Secondary 34B20, 47A10. | |||||||||
| DOI: | 10.1090/S0002-9947-96-01525-5 | |||||||||
| Record Number: | CaltechAUTHORS:20120208-090710174 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20120208-090710174 | |||||||||
| 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. | |||||||||
| ID Code: | 29189 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 08 Feb 2012 17:33 | |||||||||
| Last Modified: | 09 Nov 2021 17:04 |
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