Uniform spectral properties of one-dimensional quasicrystals, III. $\alpha$-continuity

Abstract

We study the spectral properties of discrete one-dimensional Schrödinger operators with Sturmian potentials. It is shown that the point spectrum is always empty. Moreover, for rotation numbers with bounded density, we establish purely $\alpha$-continuous spectrum, uniformly for all phases. The proofs rely on the unique decomposition property of Sturmian potentials, a mass-reproduction technique based upon a Gordon-type argument, and on the Jitomirskaya-Last extension of the Gilbert-Pearson theory of subordinacy.

12 pages

References in corpus (4)

• Eigenfunctions, transfer matrices, and absolutely continuous spectrum of one-dimensional Schrodinger operators
• Gordon-type arguments in the spectral theory of one-dimensional quasicrystals
• Uniform spectral properties of one-dimensional quasicrystals, II. The Lyapunov exponent
• Hierarchical structures in Sturmian dynamical systems

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