Simon, Barry (1996) Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators. Proceedings of the American Mathematical Society, 124 (11). pp. 3361-3369. ISSN 0002-9939. doi:10.1090/S0002-9939-96-03599-X. https://resolver.caltech.edu/CaltechAUTHORS:20180511-162701951
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Abstract
We provide a short proof of that case of the Gilbert-Pearson theorem that is most often used: That all eigenfunctions bounded implies purely a.c. spectrum. Two appendices illuminate Weidmann's result that potentials of bounded variation have strictly a.c. spectrum on a half-axis.
| Item Type: | Article | ||||||
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| Additional Information: | © Copyright 1996 Barry Simon. Communicated by: Palle E. T. Jorgensen. Received by the editors April 3, 1995 and, in revised form, April 24, 1995. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9401491. The Government has certain rights in this material. | ||||||
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| Issue or Number: | 11 | ||||||
| Classification Code: | MSC (1991): Primary 34L40 | ||||||
| DOI: | 10.1090/S0002-9939-96-03599-X | ||||||
| Record Number: | CaltechAUTHORS:20180511-162701951 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180511-162701951 | ||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 86383 | ||||||
| Collection: | CaltechAUTHORS | ||||||
| Deposited By: | George Porter | ||||||
| Deposited On: | 14 May 2018 17:18 | ||||||
| Last Modified: | 15 Nov 2021 20:38 |
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