Multilinear Fourier multipliers of a locally compact group

Master thesis (2024)

Authors

K. Veerkamp Electrical Engineering, Mathematics and Computer Science

Contributors

M.P.T. Caspers Analysis - EEMCS (supervisor 1)
F.M. de Oliveira Filho Discrete Mathematics and Optimization - EEMCS (supervisor 2)
B. Janssens Analysis - EEMCS (supervisor 2)
Faculty
Electrical Engineering, Mathematics and Computer Science
Convolution Schur multipliers Fourier multipliers Lattice Group von Neumann algebras Locally compact groups Multilinear Fourier multipliers Weak amenability Fourier algebra Multilinear Completely bounded
More Info
expand_more

Published Date

04-06-2024

Language

English

Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Faculty

Electrical Engineering, Mathematics and Computer Science

Abstract

In his paper "Group C*-algebras without the completely bounded approximation property", Haagerup proves several important results about the weak amenability of locally compact groups. Among these, is the result that a lattice in a second-countable, unimodular, locally compact group is weakly amenable if and only if the surrounding group itself is weakly amenable. A key ingredient in his proof is a method of using (linear) completely bounded Fourier multipliers on the lattice to construct (linear) completely bounded Fourier multipliers on the surrounding group. We use a similar approach to construct multilinear completely bounded Fourier multipliers on the group from multilinear completely bounded Fourier multipliers on the lattice. Our construction is both bounded in the norm of completely bounded Fourier multipliers and preserves uniform convergence on compact sets for bounded nets. We also prove an equivalent characterization of weak amenability where the Fourier algebra is replaced by the space of continuous and compactly supported $n$-linear Fourier multiplier symbols.