Kiselev, Alexander and Last, Yoram and Simon, Barry (1998) Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators. Communications in Mathematical Physics, 194 (1). pp. 1-45. ISSN 0010-3616. doi:10.1007/s002200050346. https://resolver.caltech.edu/CaltechAUTHORS:20180320-092711915
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Abstract
Using control of the growth of the transfer matrices, we discuss the spectral analysis of continuum and discrete half-line Schrödinger operators with slowly decaying potentials. Among our results we show if, where W has compact support and, then H has purely a.c. (resp. purely s.c.) spectrum on (O,∞) if). For λn^({-1/2}) ɑ_n potentials, where a n are independent, identically distributed random variables with E(ɑ_n ) = O, E(ɑ^2_n)=1, and λ < 2, we find singular continuous spectrum with explicitly computable fractional Hausdorff dimension.
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Additional Information: | © 1998 Springer-Verlag. Received: 8 April 1997. Accepted: 19 June 1997. Research supported in part by NSF Grant No. DMS-9022140. 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 Analysis; Compact Support; Continuous Spectrum; Hausdorff Dimension; Transfer Matrice | ||||||||||||
Issue or Number: | 1 | ||||||||||||
DOI: | 10.1007/s002200050346 | ||||||||||||
Record Number: | CaltechAUTHORS:20180320-092711915 | ||||||||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20180320-092711915 | ||||||||||||
Official Citation: | Kiselev, A., Last, Y. & Simon, B. Comm Math Phys (1998) 194: 1. https://doi.org/10.1007/s002200050346 | ||||||||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||||||||
ID Code: | 85373 | ||||||||||||
Collection: | CaltechAUTHORS | ||||||||||||
Deposited By: | Ruth Sustaita | ||||||||||||
Deposited On: | 20 Mar 2018 17:08 | ||||||||||||
Last Modified: | 15 Nov 2021 20:28 |
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