Intrinsic pseudo-differential calculi on any compact Lie group (Q491519)

The author describes a representation-theoretic construction of a pseudo-differential calculus on a compact Lie group \(G\). Characterizing the notion of a pseudo-differential calculus in Definition 1 by a list of basic properties, the Main Theorem 3.13 states that her construction satisfies these conditions. The proof of this result, given in Sections 4--8, forms the bulk of the paper. As a consequence, this calculus coincides with the (localized) pseudo-differential calculus of Hörmander, which can be defined on \(G\) viewing \(G\) as a compact manifold.