Etude du Spectre Pour Certains Noyaux sur un Arbre

  • Ferdaous Kellil

    ISIMM, Université de Monastir, Tunisia
  • Guy Rousseau

    Université de Lorraine, Vandoeuvre lès Nancy, France


We study in this paper the spectrum of some kernels acting on a locally finite tree, in particular those associated to an isotropic random walk on the tree with jumps of length 0, 1 or 2. Such a kernel is a function R on S_×_S where S is the set of vertices of the tree, it acts on lr(S). We always assume the kernel R to be invariant under the action of a group Λ of authomorphisms almost transitive on S. This work generalizes results of A. Figa Talamanca and T. Steger who deal with homogeneous trees and a fixed group Λ, simply transitive on S; it shows the diversity of the spectrum depending on the invariance group.

Cite this article

Ferdaous Kellil, Guy Rousseau, Etude du Spectre Pour Certains Noyaux sur un Arbre. Rend. Sem. Mat. Univ. Padova 120 (2008), pp. 29–44

DOI 10.4171/RSMUP/120-2