Dispersive PDE on noncompact symmetric spaces

Abstract: My talk will be devoted to the Schrödinger equation and to the wave equation on general Riemannian symmetric spaces of noncompact type. The main issue consists in obtaining good pointwise estimates of their fundamental solutions. This is achieved by combining the inverse spherical Fourier transform with the following tools: on the one hand, a barycentric decomposition, which allows us to handle the Plancherel density as if it were a differentiable symbol, and, on the other hand, an improved Hadamard parametrix for the wave equation. As consequences, we deduce dispersive estimates and Strichartz inequalities for the linear equations, which are stronger than their Euclidean counterparts, as well as better results for the nonlinear equations. All this is based on joint works including several collaborators: Vittoria Pierfelice in rank one, Hong-Wei Zhang in higher rank, with contributions by Maria Vallarino and Stefano Meda.

analysis of PDEsnumber theoryrepresentation theory

Audience: researchers in the topic

Harmonic Analysis and Symmetric Spaces 2021