 95355 Last Y.
 Almost Everything about the Almost Mathieu Operator I
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Jul 5, 95

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Abstract. We review some aspects of the spectral theory of the Almost Mathieu
operator (acting on $\ell^2(Z)$):
$$(H_{\alpha, \lambda, \theta} u)(n) =
u(n+1)+u(n1)+\lambda\cos (2\pi\alpha n+\theta)u(n)\;,$$
where $\alpha,\lambda,\theta \in R$. We concentrate on the spectrum
as a set, and describe the partial results obtained so far on the
conjectures that, for irrational $\alpha$, it is a Cantor set and has
Lebesgue measure $42\lambda$.
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