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Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization

Del Rio, R. and Jitomirskaya, S. and Last, Y. and Simon, B. (1996) Operators with singular continuous spectrum, IV. Hausdorff dimensions, rank one perturbations, and localization. Journal d’Analyse Mathématique, 69 (1). pp. 153-200. ISSN 0021-7670. http://resolver.caltech.edu/CaltechAUTHORS:20180315-134316740

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Abstract

Although concrete operators with singular continuous spectrum have proliferated recently [7, 11, 13, 17, 34, 35, 37, 39], we still don't really understand much about singular continuous spectrum. In part, this is because it is normally defined by what it isn't─neither pure point nor absolutely continuous. An important point of view, going back in part to Rogers and Taylor [27, 28], and studied recently within spectral theory by Last [22] (also see references therein), is the idea of using Hausdorff measures and dimensions to classify measures. Our main goal in this paper is to look at the singular spectrum produced by rank one perturbations (and discussed in [7, 11, 33]) from this point of view.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1007/BF02787106DOIArticle
https://link.springer.com/article/10.1007/BF02787106PublisherArticle
http://rdcu.be/I8QGPublisherFree ReadCube access
ORCID:
AuthorORCID
Simon, B.0000-0003-2561-8539
Additional Information:© 1996 Hebrew University of Jerusalem. Received July 1, 1995. This material is based upon work supported by the National Science Foundation under Grant No. DMS-9208029. The Government has certain rights in this material. 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-9208029
NSFDMS-9401491
Subject Keywords:Spectral Measure; Hausdorff Dimension; Dynamical Localization; Point Spectrum; Anderson Model
Record Number:CaltechAUTHORS:20180315-134316740
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180315-134316740
Official Citation:del Rio, R., Jitomirskaya, S., Last, Y. et al. J. Anal. Math. (1996) 69: 153. https://doi.org/10.1007/BF02787106
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85338
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:16 Mar 2018 15:27
Last Modified:16 Mar 2018 15:27

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