Dirichlet-to-Robin maps on finite networks

Abstract

Our aim is to characterize those matrices that are the response matrix of a semi-positive definite Schr?dinger operator on a circular planar network. Our findings generalize the known results and allow us to consider both nonsingular and non diagonally dominant matrices as response matrices. To this end, we define the Dirichlet-to-Robin map associated with a Schr?dinger operator on general networks, and we prove that it satisfies the alternating property which is essential to characterize the response matrices.