Determinants of Classical SG-pseudodifferential Operators

Abstract

We introduce a generalized trace functional TR in the spirit of Kontsevich and Vishik's canonical trace for classical SG-pseudodifferential operators on and suitable manifolds, using a finite-part integral regularization technique. This allows us to define a zeta-regularized determinant for parameter-elliptic operators , , . For , the asymptotics of as and of as are derived. For suitable pairs we show that coincides with the so-called relative determinant .