The index of cusp operators on manifolds with corners (Q1597447)

The aim of the paper is to express the index of cusp Fredholm operators on compact manifolds in terms of regularized ``trace'' functionals. First, the authors recall the notation of cusp structure on compact manifolds with corners and cusp differential operators. The construction of an algebra of cusp pseudodifferential operators and the Fredholm criterion for fully elliptic operators acting on suitable Sobolev spaces are described. Then ``trace'' functionals of the cusp calculus are introduced. This functionals are used in the formula of index of fully elliptic pseudodifferential operators proved in the last section. The formula is similar to the residue trace of Wodzicki and Guillemin.