Gesztesy, F. and Holden, H. and Simon, B. (1995) Absolute Summability of the Trace Relation for Certain Schrödinger Operators. Communications in Mathematical Physics, 168 (1). pp. 137-161. ISSN 0010-3616. doi:10.1007/BF02099586. https://resolver.caltech.edu/CaltechAUTHORS:20180315-131739823
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Abstract
A recently established general trace formula for one-dimensional Schrödinger operators is systematically studied in the context of short-range potentials, potentials which approach different spatial asymptotes sufficiently fast, and appropriate impurity (defect) interactions in one-dimensional solids. We prove the absolute summability of the trace formula and establish its connections with scattering quantities, such as reflection coefficients, in each case.
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| Additional Information: | © 1995 Springer-Verlag. Received: 4 February 1994. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material. We would like to thank Z. Zhao for numerous helpful discussions. F.G. is indebted to the Department of Mathematical Sciences of the University of Trondheim, Norway, and the Department of Mathematics at Caltech, Pasadena, CA for the hospitality extended to him in the summer of 1993. Support by the Norwegian Research Council (NFR) and by Caltech is gratefully acknowledged. H.H. is grateful to the Norwegian Research Council (NFR) for support. Communicated by T. Spencer. | |||||||||||||||
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| Subject Keywords: | Reflection; Neural Network; Statistical Physic; Complex System; Nonlinear Dynamics | |||||||||||||||
| Issue or Number: | 1 | |||||||||||||||
| DOI: | 10.1007/BF02099586 | |||||||||||||||
| Record Number: | CaltechAUTHORS:20180315-131739823 | |||||||||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180315-131739823 | |||||||||||||||
| Official Citation: | Gesztesy, F., Holden, H. & Simon, B. Commun.Math. Phys. (1995) 168: 137. https://doi.org/10.1007/BF02099586 | |||||||||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||||||||
| ID Code: | 85334 | |||||||||||||||
| Collection: | CaltechAUTHORS | |||||||||||||||
| Deposited By: | Ruth Sustaita | |||||||||||||||
| Deposited On: | 16 Mar 2018 14:38 | |||||||||||||||
| Last Modified: | 15 Nov 2021 20:27 |
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