Given a subset
Λ
\Lambda
of
Z
+
≔
{
0
,
1
,
2
,
…
}
\mathbb Z_+≔\{0,1,2,\dots \}
, let
H
∞
(
Λ
)
H^\infty (\Lambda )
denote the space of bounded analytic functions
f
f
on the unit disk whose coefficients
f
^
(
k
)
\widehat f(k)
vanish for
k
∉
Λ
k\notin \Lambda
. Assuming that either
Λ
\Lambda
or
Z
+
∖
Λ
\mathbb Z_+\setminus \Lambda
is finite, we determine the extreme points of the unit ball in
H
∞
(
Λ
)
H^\infty (\Lambda )
.