Abstract
Given a linear functional
U
in the linear space
P
of polynomials in one variable with complex coefficients, under certain conditions, we give a new representation of a
U
by a discrete measure. Finally, as an application for arbitrary
q
∈
C
with
|
q
|
<
1
,
we can represent the linear functionals
δ
′
and
2
q
δ
-
δ
′
′
by means of discrete measures with
supp
=
{
q
-
k
,
k
≥
0
}
,
with
δ
the Dirac functional defined by
⟨
δ
,
p
⟩
:
=
p
(
0
)
,
p
∈
P
.