On a class of pseudodifferential operators on the product of compact Lie groups

TL;DR

This paper develops a global bisingular pseudodifferential calculus on products of compact Lie groups, extending harmonic analysis techniques to analyze operators in this setting.

Contribution

It introduces a new pseudodifferential calculus framework on product compact Lie groups based on harmonic analysis, generalizing previous local approaches.

Findings

Established a global calculus for bisingular pseudodifferential operators

Extended harmonic analysis methods to the setting of product Lie groups

Provided tools for analyzing operators on compact Lie group products

Abstract

In this paper a bisingular pseudodifferential calculus, along the lines of the one introduced by L. Rodino in [12], is developed in the global setting of a product of compact Lie groups. The approach follows that introduced by M. Ruzhansky and V. Turunen [13] (see also V. Fischer [5]), in that it exploits the harmonic analysis of the groups involved.