Abstract
Let
(
C
∞
,
⊛
)
denote the algebra of infinitely differentiable functions in
[
0
,
1
]
with Duhamel product
(
f
⊛
g
)
=
d
d
x
∫
0
x
f
(
x
−
t
)
g
(
t
)
d
t
as multiplication. We describe all the closed ideals in
(
C
∞
,
⊛
)
. As a consequence we obtain that the integration operator
I
,
(
I
f
)
(
x
)
=
∫
0
x
f
(
t
)
d
t
, is unicellular in the space
C
∞
[
0
,
1
]
, which is the solution of a long-standing problem.