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Bounded eigenfunctions and absolutely continuous spectra for one-dimensional Schrödinger operators

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. 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
Related URLs:
URLURL TypeDescription
https://doi.org/10.1090/S0002-9939-96-03599-XDOIArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
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.
Funders:
Funding AgencyGrant Number
NSFDMS-9401491
Issue or Number:11
Classification Code:MSC (1991): Primary 34L40
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:03 Oct 2019 19:43

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