Let Bτ
denote the class of entire functions of exponential type
τ (>0) bounded on the real axis. For the
function f ∊ Bτ
we have the interpolation formula [1, p.
143]
1.1
where t, γ are real
numbers and is the so called
conjugate function of f. Let us put
1.2
The function Gγ,f
is a periodic function of α, with period 2. For
t = 0 (the general case is obtained by translation)
the righthand member of (1) is 2τGγ,f
(1). In the following paper we suppose that
f satisfies an additional hypothesis of the form
f(x) =
O(|x|-ε), for some ε >
0, as x → ±∞ and we give an integral representation of
Gγ,f(α) which is valid for 0
≦ α ≦ 2.