An operator algebra on manifolds with cusp-type singularities (Q1386839)

The algebra of pseudodifferential operators on an arbitrary smooth manifold with a finite number of points of cusp-type is investigated. A family of local cusp algebras is constructed and the local Fredholm properties are established. The Fredholm property (global) is a direct consequence of the existence of local regularizers. The resurgent character of solutions is proved for elliptic pseudodifferential equations with infinitely many exponentially flat near-singular points on the right-hand side.