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Modified Prüfer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schrödinger Operators

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.

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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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Simon, Barry0000-0003-2561-8539
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
Record Number:CaltechAUTHORS:20180320-092711915
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Official Citation:Kiselev, A., Last, Y. & Simon, B. Comm Math Phys (1998) 194: 1.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85373
Deposited By: Ruth Sustaita
Deposited On:20 Mar 2018 17:08
Last Modified:15 Nov 2021 20:28

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