Symbol of a functional-pseudodifferential operator on a compact manifold (Q1119247)

Let X be an \(\ell\)-dimensional \(C^{\infty}\)-smooth compact Riemannian manifold, E be a complex vector bundle over X, \(H^ s(E)\) be the Sobolev space of sections of E, G be subgroup of Diff(X), \(\{T_ g\}_{g\in G}\) be standard representation of G in \(H^ s(E)\). This article is devoted to study the space of G-pseudodifferential operators: \(b=\sum a_ gT_ g\), where \(a_ g\in P_ X\), \(P_ X\) is the algebra of pseudodifferential operators of degree 0 on X. The aim of this article is to construct the symbolic calculus for this class of operators.