English

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 GG.

Keywords

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

R2 v1 2026-06-23T15:21:08.495Z