Invariance of the cone algebra without asymptotics (Q1126454)

The author considers a cone algebra of Mellin operators defined on a manifold with conical singularities. Let the manifold be the cylinder \(X\times \overline{\mathbb{R}}_+\), where \(X\) is a compact smooth manifold without boundary. Then the Mellin operator has a symbol that is a smooth function on \(\mathbb{R}_+\times \mathbb{R}_+\) with values in an algebra of pseudodifferential operators on \(X\). The main result of the paper is the invariance of this cone algebra under smooth change of variables \((x,t)\to(\chi(x,t),\sigma(x,t))\) in the cylinder \(X\times \overline{\mathbb{R}}_+\).