Communications in Mathematical Physics

, Volume 192, Issue 1, pp 169–182

α-Continuity Properties of One-Dimensional Quasicrystals

Authors

  • David Damanik
    • Fachbereich Mathematik, Johann Wolfgang Goethe-Universität, 60054 Frankfurt/Main, Germany

DOI: 10.1007/s002200050295

Cite this article as:
Damanik, D. Comm Math Phys (1998) 192: 169. doi:10.1007/s002200050295

Abstract:

We apply the Jitomirskaya-Last extension of the Gilbert-Pearson theory to discrete one-dimensional Schrödinger operators with potentials arising from generalized Fibonacci sequences. We prove for certain rotation numbers that for every value of the coupling constant, there exists an α > 0 such that the corresponding operator has purely α-continuous spectrum. This result follows from uniform upper and lower bounds for the ∥⋅∥L-norm of the solutions corresponding to energies from the spectrum of the operator.

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© Springer-Verlag Berlin Heidelberg 1998