Equivalence of resolvent and scattering resonances on quantum graphs

Abstract

We discuss resonances for Schrödinger operators on metric graphs which consists of a finite compact part and a finite number of halflines attached to it; the vertex coupling is assumed to be of the $δ$-type or certain modifications of it. Using exterior complex scaling on the graph we show that the resolvent and scattering resonances coincide in this case.

9 pages, AMS-LaTeX, written for proceedings of a conference in honour of J.-M. Combes, Cergy-Pontoise, September 2006