Properties and applications of the vector Harper operator / Stuart Yates.

Abstract

This thesis examines a vector-valued generalization of the Harper operator on a graph with a free action of a discrete group, the scalar version of which was defined by Sunada. A spectral approximation result is obtained for the vector Harper operator (and more generally for a large class of operators) which states that when the group is amenable, the spectral density function can be approximated by the average spectral density functions of finite approximations to the operator with arbitrary boundary conditions.