Wiener algebra

Summary

The Wiener algebra $A(\mathbb{T})$ is the set of continuous periodic functions with an absolutely convergent Fourier series. Its norm is the sum of the absolute values of the Fourier coefficients. With pointwise multiplication it is a commutative Banach algebra, isometrically isomorphic to the sequence algebra $\ell^1(\Z)$ with convolution. It is the setting of Wiener's lemma and a basic example in the Gelfand theory of commutative Banach algebras.