Beurling algebra

In mathematics, the term Beurling algebra is used for different algebras introduced by Arne Beurling (1949), usually it is an algebra of periodic functions with Fourier series

Example We may consider the algebra of those functions f where the majorants

of the Fourier coefficients a_n are summable. In other words

Example We may consider a weight function w on ${\displaystyle \mathbb {Z} }$ such that

in which case ${\displaystyle A_{w}(\mathbb {T} )=\{f:f(t)=\sum _{n}a_{n}e^{int},\,\|f\|_{w}=\sum _{n}|a_{n}|w(n)<\infty \}\,(\sim \ell _{w}^{1}(\mathbb {Z} ))}$ is a unitary commutative Banach algebra.

...
Wikipedia