Quantisation on a manifold with singular edge

Abstract

Boundary value problems and mixed problems play a role in many applications of physics, cf. (Harutyunyan et al., Elliptic mixed, transmission and singular crack problems, 2008), and parametrices and asymptotics of solutions may be expressed within suitable pseudo-differential algebras. The boundary-wedge approach of Schulze (Pseudo-differential operators on manifolds with edges, 1989), Schulze (Ann Glob Anal Geom 8(3):261–297, 1990) belongs to the calculus on singular manifolds. The present article continues this concept and develops new quantisations in the framework of operators on manifolds with singular edges.