Gesztesy, Fritz and Simon, Barry (2000) On Local Borg–Marchenko Uniqueness Results. Communications in Mathematical Physics, 211 (2). pp. 273-287. ISSN 0010-3616. doi:10.1007/s002200050812. https://resolver.caltech.edu/CaltechAUTHORS:20170801-072515055
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Abstract
We provide a new short proof of the following fact, first proved by one of us in 1998: If two Weyl–Titchmarsh m-functions, m_j(z), of two Schrödinger operators, H_j = -d^2/dx^2 + q_j, j = 1,2 in L^2((O,R)), O < R ≤ ∞, are exponentially close, that is, |m_1(z) - m_2(z)|_|z|→∞ = O(e^(-2 IM(z^1/2)a), O < ɑ <R, then q_1 = q_2 a.e. on [O,ɑ]. The result applies to any boundary conditions at x = O and x = R and should be considered a local version of the celebrated Borg–Marchenko uniqueness result (which is quickly recovered as a corollary to our proof). Moreover, we extend the local uniqueness result to matrix-valued Schrödinger operators.
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Additional Information: | © 2000 Springer-Verlag. Received: 22 October 1999; Accepted: 2 November 1999. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9707661. F. G. thanks T. Tombrello for the hospitality of Caltech where this work was done. | ||||||||||||
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Issue or Number: | 2 | ||||||||||||
DOI: | 10.1007/s002200050812 | ||||||||||||
Record Number: | CaltechAUTHORS:20170801-072515055 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170801-072515055 | ||||||||||||
Official Citation: | Gesztesy, F. & Simon, B. Comm Math Phys (2000) 211: 273. https://doi.org/10.1007/s002200050812 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 79655 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Ruth Sustaita | ||||||||||||
Deposited On: | 01 Aug 2017 15:55 | ||||||||||||
Last Modified: | 15 Nov 2021 17:49 |
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