Algebras of Pseudodifferential Operators near Edge and Corner Singularities

This research monograph deals with analysis on manifolds with singularities. More precisely, it presents pseudodifferential operators near edges and corners. In particular, it considers parameter-dependent edge operators and edge operators of Mellin type. The investigation of such operator families is necessary to construct operator algebras on manifolds with higher singularities. A self-contained exposition in Mellin techniques and pseudodifferential operators with operator-valued symbols is given. The algebra of parameter-dependent edge operators is constructed. Finally, Mellin operators near corner singularities are investigated.
The focus is on elliptic theory. Elliptic operators on manifolds with edges are constructed as well as parametrices to elliptic elements. The equivalence of ellipticity and the Fredholm property is shown. Close to corner singularities, edge operators of Mellin type are defined, a pseudodifferential calculus is presented and parametrices are constructed. Asymptotics are treated using analytic functions and the concept of continuous asymptotic types.