Cone pseudodifferential operators in the edge symbolic calculus
José Ignacio Burgos Gil, B.‐W. Schulze, Jörg Seiler · Institutional Repositories DataBase (IRDB) · 2000
We consider a class of parameter-dependent pseudodifferential operators on the model cone (with smooth compact cross section) of a wedge, which is shown to be a symmetric algebra. Its construction relies on a particular quantization of corresponding edgedegenerate symbols, based on the Mellin transform along the axial variable of the cone. These operator families are essential for the analysis of pseudodifferential operators on manifolds with edges. In particular, they serve as symbols for Laplace-Beltrami operators to wedge metrics and their parametrices if the parameter is treated as the covariable. AMS Classification: 58G20, 58G99, 35S15 Introduction The present paper studies an algebra of parameter-dependent pseudodifferential operators on a manifold with conical singularities, where the parameters are involved as covariables in a specific degenerate way. Such operator families serve as an adequate symbol class for pseudodifferential operators on manifolds with edges. Also the st...