Beurling-Fourier Algebras and Complexification
Functional Analysis
2022-07-26 v3
Abstract
In this paper, we develop a new approach that allows to identify the Gelfand spectrum of weighted Fourier algebras as a subset of an abstract complexification of the corresponding group for a wide class of groups and weights. This generalizes recent related results of Ghandehari-Lee-Ludwig-Spronk-Turowska (Adv. Math. 2021) about the spectrum of Beurling-Fourier algebras on some Lie groups. In the case of discrete groups we show that the spectrum of Beurling-Fourier algebra is homeomorphic to .
Cite
@article{arxiv.2005.02821,
title = {Beurling-Fourier Algebras and Complexification},
author = {Olof Giselsson and Lyudmila Turowska},
journal= {arXiv preprint arXiv:2005.02821},
year = {2022}
}
Comments
The previous paper is splited in two parts. This is the first part. It also contains numerous changes and new results