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

  title={Modified Pr{\"u}fer and EFGP Transforms and the Spectral Analysis of One-Dimensional Schr{\"o}dinger Operators
  author={Alexander V. Kiselev and Yoram Last and Barry Simon},
  journal={Communications in Mathematical Physics},
Abstract:Using control of the growth of the transfer matrices, wediscuss 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 (0,∞) if ). For λn{-1/2}an potentials, where an are independent, identically distributed random variables with E(an) = 0, E(a2n)=1, and λ < 2, we find singular continuous spectrum with… 
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