Mathematics Colloquia and Seminars
A Quantitative Stability Theorem for Convolution on the Heisenberg GroupPDE and Applied Math Seminar
|Speaker:||Kevin O'Neill, UC Davis|
|Start time:||Fri, May 8 2020, 3:00PM|
Although convolution on Euclidean space and the Heisenberg group satisfy the same $L^p$ bounds with the same optimal constants, the former has maximizers while the latter does not. However, as work of Christ has shown, it is still possible to characterize near-maximizers. Specifically, any near-maximizing triple of the trilinear form for convolution on the Heisenberg group must be close to a particular type of triple of ordered Gaussians after adjusting by symmetry. In this talk, we will use the expansion method to prove a quantitative version of this characterization.