---
abstract: 'We investigate the distribution of the resonances near spectral thresholds of Laplace operators on regular tree graphs with $k$-fold branching, $k \geq 1$, perturbed by nonself-adjoint exponentially decaying potentials. We establish results on the absence of resonances which in particular involve absence of discrete spectrum near some sectors of the essential spectrum of the operators.'
address:
- 'Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago de Chile'
- 'Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago de Chile'
- 'Departamento de Matemáticas, Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Vicuña Mackenna 4860, Santiago de Chile'
author:
- 'Olivier <span style="font-variant:small-caps;">Bourget</span>'
- 'Diomba <span style="font-variant:small-caps;">Sambou</span>'
- 'Amal <span style="font-variant:small-caps;">Taarabt</span>'
title: Resonances on regular tree graphs
---

Introduction {#s1}
============

A great interest has been focused in the last decades on spectral analysis of Laplace operators on regular trees. This includes local perturbations [@al; @af], random settings [@kl; @aw; @ai; @fr; @fr1; @sh] (see also the references therein), and quantum ergodicity regimes [@am]. For complementary results, we refer the reader to the papers [@br; @bk; @ro1; @ro2; @rr], and for the relationships between the Laplace 