Max Carter: "Weighted Orlicz *-algebras on locally elliptic groups "

mardi 15 avr. 2025, 14:00 → 15:00 Europe/Paris

435 (UMPA)

If $G$ is a locally compact group, then $L^p(G)$ is closed under convolution, and hence a Banach algebra, if and only if $G$ is compact. In the case that $G$ is a non-compact but $\sigma$-compact group, there always exists a weight on $G$ such that the corresponding weighted $L^p$-space is a Banach algebra under convolution. One can go even further than this and study Banach algebras on locally compact groups which are of the form of a weighted Orlicz space (an Orlicz space is a natural generalisation of an $L^p$-space).

 

In this talk I will discuss a recent project studying the harmonic analysis of weighted Orlicz *-algebras on "locally elliptic" groups.  A locally elliptic group is a locally compact group that can be written as a countable ascending union of compact open subgroups. They are a natural class of groups that appear in the theory of totally disconnected groups, and include, for example, locally finite discrete groups and unipotent algebraic groups over non-archimedean local fields. I will talk about properties concerning a generalised Fourier transform on these algebras, their spectral theory, and discuss how these algebras can be used to study the unitary representation theory of locally elliptic groups.

 

The talk will be based on the following arXiv preprint: https://arxiv.org/abs/2503.20735.