Geodesic
Representation Formulas for Integrable and Entire Functions of Exponential Type I
Canadian journal of mathematics, Tome 40 (1988) no. 4, pp. 1010-1024

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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. 
Frappier, Clément. Representation Formulas for Integrable and Entire Functions of Exponential Type I. Canadian journal of mathematics, Tome 40 (1988) no. 4, pp. 1010-1024. doi: 10.4153/CJM-1988-040-3
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