Gesztesy, F. and Holden, H. and Simon, B. and Zhao, Z. (1996) A Trace Formula for Multidimensional Schrödinger Operators. Journal of Functional Analysis, 141 (2). pp. 449-465. ISSN 0022-1236. doi:10.1006/jfan.1996.0137. https://resolver.caltech.edu/CaltechAUTHORS:20170912-095106346
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Abstract
We prove multidimensional analogs of the trace formula obtained previously for one-dimensional Schrödinger operators. For example, letVbe a continuous function on [0, 1]^ν⊂R^ν. For A⊂{1,…,ν}, let −Δ_A be the Laplace operator on [0, 1]^ν with mixed Dirichlet–Neumann boundary conditions[formula]Let |A|= number of points inA. Then we'll prove that[formula]with ⦠V⦔ the average of Vat the 2^ν corners of [0, 1]^ν.
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| Additional Information: | © 1996 Academic Press, Inc. Received 7 April 1995. 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 thank Peter Lax for telling us of his work prior to publication. F. G. is indebted to M. Aschbacher and G. Neugebauer for the hospitality at Caltech where some of this work was done. F. G. and H. H. were also supported in part by the Norwegian Research Council for Science and the Humanities (NAVF). | |||||||||
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| Issue or Number: | 2 | |||||||||
| DOI: | 10.1006/jfan.1996.0137 | |||||||||
| Record Number: | CaltechAUTHORS:20170912-095106346 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170912-095106346 | |||||||||
| Official Citation: | F Gesztesy, H Holden, B Simon, Z Zhao, A Trace Formula for Multidimensional Schrödinger Operators, Journal of Functional Analysis, Volume 141, Issue 2, 1996, Pages 449-465, ISSN 0022-1236, http://dx.doi.org/10.1006/jfan.1996.0137. (http://www.sciencedirect.com/science/article/pii/S0022123696901378) | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 81345 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Ruth Sustaita | |||||||||
| Deposited On: | 12 Sep 2017 18:16 | |||||||||
| Last Modified: | 15 Nov 2021 19:42 |
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