Toolbox of Para-differential Calculus on Compact Lie Groups

2023/10/10 by Chengyang Shao, Shao, Chengyang · 2 citations
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Homotopy and Cohomology in Algebraic Topology #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2310.06806

Abstract

This paper provides a toolbox of para-differential calculus on compact Lie groups. The toolbox is based on representation theory of compact Lie groups and contains exact formulas of symbolic calculus. Para-differential operators are constructed in a global, coordinate-free manner, giving lower order terms in symbolic calculus a clear form. The toolbox helps to understand non-local, nonlinear differential operators defined on certain manifolds with high symmetry.

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