Green operators of networks with a new vertex

摘要

Any elliptic operator defines an automorphism on the orthogonal subspace to the eigenfunctions associated with the lowest eigenvalue, whose inverse is the orthogonal Green operator. In this study, we show that elliptic Schrodinger operators on networks that have been obtained by adding a new vertex to a given network, can be seen as perturbations of the Schrodinger operators on the initial network. Therefore, the Green function of the new network can be computed in terms of the Green function of the original network. (C) 2015 Elsevier Inc. All rights reserved.