Fourier series and twisted C*-crossed products

TL;DR

This paper explores Fourier analysis techniques within the framework of reduced twisted C*-crossed products, focusing on convergence, multipliers, and ideal structures using advanced representation theory.

Contribution

It introduces new methods for analyzing Fourier series and multipliers in twisted C*-crossed products, leveraging covariant and equivariant representations.

Findings

Established norm-convergence results for Fourier series

Analyzed multipliers and summation processes in twisted C*-crossed products

Provided insights into the ideal structure of these C*-algebras

Abstract

This paper is an invitation to Fourier analysis in the context of reduced twisted C*-crossed products associated with discrete unital twisted C*-dynamical systems. We discuss norm-convergence of Fourier series, multipliers and summation processes. Our study relies in an essential way on the (covariant and equivariant) representation theory of C*-dynamical systems on Hilbert C*-modules. It also yields some information on the ideal structure of reduced twisted C*-crossed products.