Ja n 20 02 Schrödinger operators on fractal lattices with random blow - ups Christophe Sabot
نویسنده
چکیده
Starting from a finitely ramified self-similar set X we can construct an unbounded set X<∞> by blowing-up the initial set X. We consider random blow-ups and prove elementary properties of the spectrum of the natural Laplace operator on X<∞> (and on the associated lattice). We prove that the spectral type of the operator is almost surely deterministic with the blow-up and that the spectrum coincides with the support of the density of states almost surely (actually our result is more precise). We also prove that if the density of states is completely created by the socalled Neuman-Dirichlet eigenvalues, then almost surely the spectrum is pure point with compactly supported eigenfunctions. AMS classification: 82B44(60H25,28A80)
منابع مشابه
Schrr Odinger Operators on Fractal Lattices with Random Blow-ups
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