报告题目：Local and Multilinear Noncommutative De Leeuw Theorems

报告时间：2022-12-02  17:00 - 18:30

报告人：Prof.Martijn Caspers   Delft University of Technology

ZOOMID：885 517 8417   密码：whu2022

Abstract：In 1965 Karel de Leeuw proved several fundamental theorems that relate Fourier multipliers on with Fourier multipliers on the torus. These theorems are widely used in harmonic analysis. One of De Leeuw his most important contributions is the restriction theorem that states that if a continuous symbol on is restricted to then the associated Fourier multipliers of the symbols decrease in bound under this restriction. These theorems have soon been generalized to abelian locally compact groups and much more recently to pairs of groups (Gamma, G) where G has small almost invariant neighbourhoods with respect to a discrete subgroup Gamma (by C, Parcet, Perrin and Ricard). In particular if Gamma is amenable the theorem is applicable. In the current talk we show how to obtain a De Leeuw restriction theorem for general pairs (Gamma, G) where Gamma is a discrete subgroup of G and specify the theorem for the case (SLn(Z), SLn(R)), or in fact any reductive Lie group G with Gamma arbitrary. We also prove the multilinear noncommutative de Leeuw restriction theorem. This is joint work with Bas Janssens, Amudhan Krishnaswamy-Usha and Lukas Miaskiwskyi.