Fourier restriction bounds on compact symmetric spaces

Abstract: In this talk I will make a survey of bounds of "Fourier restriction" type on compact Lie groups and more generally compact globally symmetric spaces. These include Laplace-Beltrami eigenfunction bound, Strichartz estimate for the Schrodinger equation, and joint eigenfunction bound for invariant differential operators. Optimal bounds are all open, for which a more refined combination of Lie theory and analysis would be needed.

analysis of PDEsnumber theoryrepresentation theory

Audience: researchers in the topic

Harmonic Analysis and Symmetric Spaces 2021