Exponentially decaying eigenvectors for certain almost periodic operators
نویسنده
چکیده
For every point χ in the spectrum of the operator (h(δ)ξ) = ξn+1 + ξn−1 + β ( δe + δe ) ξn on l(Z) there exists a complex number x of modulus one such that the equation ξn+1 + ξn−1 + β ( xδe + xδe ) ξn = χξn has a non-trivial solution satisfying the condition lim |n|→∞ |ξn| 1/|n| ≤ δβ provided that β, δ > 1 and α satisfies the diophantine condition lim n→∞ | sinπαn| 1 n = 1 . The parameters xδ and χ are in the range of analytic functions which are defined on a Riemann surface covering the resolvent set of the operator h(1) .
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