Seeley's Theory of Pseudodifferential Operators on Orbifolds

Abstract

We present the theory of pseudodifferential operators acting on a vector orbibundle over an orbifold, construct the zeta function of an elliptic pseudodifferential operator and show the existence of a meromorphic extension to the complex plane with at most simple poles. We give formulas for generalized densities on the orbifold whose integrals compute the residues of the zeta function.