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 Schrodinger operator on a circular planar network. Our findings generalize the known results and allow us to consider both nonsingular and Hon diagonally dominant matrices as response matrices. To this end, we define the Dirichlet-to-Robin map associated with a Schrodinger operator on general networks, and we prove that it satisfies the alternating property which is essential to characterize the response matrices.