In a joint work with R. Seeley, a calculus of weakly parametric pseudodifferential operators on closed manifolds was introduced and used to obtain complete asymptotic expansions of traces of resolvents and heat operators associated with the Atiyah- Patodi-Singer problem. The present paper establishes a generalization to pseudo differential boundary operators, defining weakly polyhomogeneous singular Green operators, Poisson operators, and trace operators associated with a manifold with boundary, as well as a suitable transmission condition for pseudodifferential operators. Full composition formulas are established for the calculus, which contains the resolvents of APS-type problems. The operators in the calculus have complete asymptotic trace expansions in the parameter (when of trace class), with polynomial and logarithmic terms. (C) 2001 Academic Press. [References: 15]
展开▼
