Topics in geometric and harmonic analysis on symmetric spaces and lie groups
George Gaylord Simpson · Sussex Research Online (University of Sussex) · 2019
In this thesis, we branch into both harmonic and geometric analysis. Within harmonic analysis, we look at differential actions Lp on hypergeometric series and Jacobi polynomials, where the latter are known to represent the zonal spherical functions on compact rank-one symmetric spaces. Within geometric analysis, we examine spherical twists as solutions to the Euler-Lagrange system associated with the Dirichlet energy and certain of its nonlinear extensions for sphere-valued mappings in suitable Sobolev spaces.