Analysis & Applications Seminar
Pointwise convergence of noncommutative Fourier series
Speaker: Simeng Wang (Université de Paris-Saclay)Date: Friday, 05 February 2021 - 11:30Place: Online - conectaha.csic.es/b/jos-vqj-olj-lpt
Abstract:
In this talk I will present some recent progress on the study of pointwise
convergence of Fourier series for compact groups, group von Neumann algebras
and quantum groups. It is well-known that a number of approximation
properties of groups can be interpreted as some summation methods and
mean convergence of the associated noncommutative Fourier series. Based
on this framework, we study the refined counterpart of pointwise convergence
of these Fourier series. In particular, we prove that for any countable discrete
amenable group, there exists a sequence of finitely supported Fourier multipliers
on the associated noncommutative Lp-spaces satisfying the pointwise
convergence for all 1 < p < oo. Our approach also yields new results for the
classical Fourier series on Euclidean spaces and compact groups. As a byproduct,
we also obtain the dimension free bounds of the noncommutative
Hardy-Littlewood maximal inequalities associated with convex bodies.
This is joint work with Guixiang Hong and Xumin Wang.
