Calculus on spaces with higher singularities
The main aim of the paper is to describe how algebras of pseudo=differential operators can be organized when the underlying manifold has singularities such as edges, boundaries or higher corners of some order. The paper consists of two chapters. The first one is devoted to the singularities of order \(k=1,2\). The authors propose a new intrinsic definition of Kegel spaces. Moreover they discuss the singular functions of asymptotics, the related ideals of operators. and the parameter dependent edge calculus. They focus on discrete asymptotics. The second chapter is devoted to singularities of order \(k>2\). The following subjects are discussed: Mellin operators of arbitrary order, compositions of symbols, higher Kegel and wedge spaces, the calculus of the operators on singular cones.
scientific article; zbMATH DE number 6818230
scientific article