Wiener algebra
= Wiener algebra
{c}
{title2=$A(\mathbb T)$}
The Wiener algebra consists of periodic <functions> with absolutely summable <Fourier coefficients>, with <norm> $\sum_k|a_k|$. Multiplication corresponds to <discrete convolution> of coefficients, so the <norm> is submultiplicative. Consequently $e^f=\sum_{n\ge0}f^n/n!$ also belongs to the algebra when $f$ does. Every such <Fourier series> is uniformly convergent and defines a <continuous function>.