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

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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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
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1090/S0002-9947-96-01525-5DOIUNSPECIFIED
http://www.ams.org/journals/tran/1996-348-01/S0002-9947-96-01525-5/home.html#AbstractPublisherUNSPECIFIED
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.
Funders:
Funding AgencyGrant Number
NSFDMS-9101715
Subject Keywords:Schrödinger operators, inverse spectral theory, Krein's spectral shift function.
Classification Code:MSC 1991: Primary 34B24, 34L05, 81Q10; Secondary 34B20, 47A10.
Record Number:CaltechAUTHORS:20120208-090710174
Persistent URL:http://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:26 Dec 2012 14:48

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