Suppose
is the set of all complex-valued functions
on the interval
of the form
(1)
|
for ,
where the
and
.
The set
with the usual pointwise operations and with the norm
(2)
|
is a commutative Banach algebra and is called the Wiener algebra.
There is an isometric isomorphism between and
given by
, where
(3)
|
with .