On the Characteristic Polynomial of the Almost Mathieu Operator
نویسنده
چکیده
Let Aθ be the rotation C*-algebra for angle θ. For θ = p/q with p and q relatively prime, Aθ is the sub-C*-algebra of Mq(C(T )) generated by a pair of unitaries u and v satisfying uv = e2πiθvu. Let hθ,λ = u+u +λ/2(v+ v) be the almost Mathieu operator. By proving an identity of rational functions we show that for q even, the constant term in the characteristic polynomial of hθ,λ is (−1) q/2(1 + (λ/2)q)− (z 1 + z 1 + (λ/2)q(z 2 + z 2 )).
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تاریخ انتشار 2006