 97426 Jitomirskaya S., Last Y.
 Anderson Localization for the Almost Mathieu Equation,
III. SemiUniform Localization, Continuity of Gaps, and Measure of the
Spectrum
(44K, LaTeX)
Jul 30, 97

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Abstract. We show that the almost Mathieu operator,
$(H_{\omega,\lambda,\theta}\Psi)(n)=\Psi(n+1) + \Psi(n1) +
\lambda\cos(\pi\omega n +\theta)\Psi(n)$, has semiuniform
(and thus dynamical) localization for $\lambda > 15$ and a.e.
$\omega,\theta$. We also obtain a new estimate on gap continuity
(in $\omega$) for this operator with $\lambda > 29$
(or $\lambda < 4/29$), and use it to prove that the measure of
its spectrum is equal to $42\lambda$ for $\lambda$ in this
range and all irrational $\omega$'s.
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