Subordinacy theory on star-like graphs

Abstract

We study Jacobi matrices on star-like graphs, which are graphs that are given by the pasting of a finite number of half-lines to a compact graph. Specifically, we extend subordinacy theory to this type of graphs, that is, we find a connection between asymptotic properties of solutions to the eigenvalue equations and continuity properties of the spectral measure with respect to the Lebesgue measure. We also use this theory in order to derive results regarding the multiplicity of the singular spectrum.