Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Pure point spectrum for the Laplacian on unbounded nested fractals


Code(s) de Classification MSC:

Résumé: We prove for the class of nested fractals introduced by Lindstr\o m (cf [15]) that the integrated density of states is completely created by the so called Neuman-Dirichlet eigenvalues. The corresponding eigenfunctions lead to eigenfunctions with compact support on the unbounded set and we prove that for a large class of blow-ups the set of Neuman-Dirichlet eigenfunctions is complete leading to a pure point spectrum with compactly supported eigenfunctions. This generalizes previous results of Teplyaev (cf [24]) on the Sierpinski Gasket. Our methods are elementary and use only symmetry arguments via the representations of the group of symmetry of the set.

Mots Clés: Spectral theory ; Schrödinger operators ; diffusions on fractals

Date: 2000-04-17

Prépublication numéro: PMA-585