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Published May 1998 | public
Journal Article

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

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.

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.

Additional details

Created:
August 22, 2023
Modified:
October 18, 2023