|Dept.||Technische Universiteit Delft|
Zoom 회의 ID: 356 501 3138 / 암호: 471247
In 1965 Karel de Leeuw proved several fundamental theorems about Fourier multipliers on the Euclidean groups (so R^n) and their restrictions to discrete subgroups. The aim of this talk is to generalize these theorems to arbitrary locally compact groups with a special focus on Lie groups. In this case Fourier multipliers are maps acting on the noncommutative Lp-space of a group von Neumann algebra. In particular we prove a De Leeuw restriction theorem for nilpotent and real reductive Lie groups. In order to do so we require a quantified version of having "small invariant neighbourhoods". We also cover multilinear versions of De Leeuw's theorem. This is based on joint work with Parcet, Perrin, Ricard from 2015 and recent joint work with Jannsens, Krishnaswamy-Usha and Miaskiwskyi from 2022.