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. https://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.
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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. | ||||||||||||
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Subject Keywords: | Spectral Measure; Hausdorff Dimension; Dynamical Localization; Point Spectrum; Anderson Model | ||||||||||||
Issue or Number: | 1 | ||||||||||||
Record Number: | CaltechAUTHORS:20180315-134316740 | ||||||||||||
Persistent URL: | https://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: | 03 Oct 2019 19:29 |
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