Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 388

Periodic weighted operators

Evgeni Korotyaev

We consider the spectral properties of the periodic weighted operator on the real line. We obtain asymptotic estimates on the fundamental solution and the Lyapunov function at high energy. This allows the construction of the quasimomentum and yields double sided estimates of the total gap length in terms of the weight as well as the asymptotics of the gap length

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