Product Description: The subject of this memoir is the spectrum of a Dirac-type operator on an odd-dimensional manifold M with boundary and, particularly, how this spectrum varies under an analytic perturbation of the operator. Two types of eigenfunctions are considered: first, those satisfying the "global boundary conditions" of Atiyah, Patodi, and Singer and second, those which extend to $L^2$ eigenfunctions on M with an infinite collar attached to its boundary...read more