In this paper we establish a relation between the support of a function f on Ω1 ⊂ R with differentiability properties of its image Tf on Ω2 ⊂ R under a linear operator T . The classical approach requires analytic continuation of the image Tf from Ω2 into the complex domain C (theorems of Paley-Wiener type [5, 6, 7]), and therefore, could not apply to functions whose images Tf are not analytic a...
