Cone pseudodifferential operators in the edge symbolic calculus

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 edge-degenerate 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.