Etude du spectre pour certains noyaux sur un arbre

Ferdaous Kellil (1) , Guy Rousseau (2)

1 Département de Mathématiques [Monastir]
2 IECN - Institut Élie Cartan de Nancy

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

Mots clés: trees; kernel; resolvent; spectrum

Domaines: Théorie des groupes [math.GR]

Ferdaous Kellil, Guy Rousseau. Etude du spectre pour certains noyaux sur un arbre. Rend. Sem. Mat. Univ. Padova, 2008, 120, pp.29-44. ⟨hal-00094415⟩