Abstract
We consider operators (parametrized by a, O, \) on /2 with matrix ojy+i + o / ; i + fl/o/y with an = COS(2TTCW + 6). If ce is a Liouville number and > 2, we prove that for a.e. 0, the operator's spectral measures are all singular continuous. We consider the operator// on l2(Z) depending upon three parameters, X, a, 0, (1) [#(X, a, 0)u] (n) = u(n + 1) + u(n 1) + X cos(2iran + 6)u(n). In this note we will sketch the proof of the following result whose detailed proof will appear elsewhere [3]. THEOREM 1. Fix a, an irrational number obeying
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