A Counterexample in the Theory of Fourier Transforms in the Complex Domain
The Borel transform of an entire function of exponential type is defined outside a closed bounded convex set D. Paley and Wiener have given a necessary and sufficient condition on the entire function F(z) such that φ(w), the Borel transform of F(z), is contained in E<sup>2</sup>(ℂ\D)...