Paley-Wiener theorems for the Hankel transformation
Two theorems of the Paley-Wiener type for the Hankel transform are established. Such theorems are known for the Fourier transform. Here the authors obtain the related results for the Hankel transform recalling a suitable space of the Frechet type introduced by Zemanian. The fact of application of this space by means of the Hankel transform onto the space of entire functions being equipped with the topology induced by a special system of norms is used. The authors introduce a new two-parameter family of spaces of entire functions bounded by a power-exponential weight. Assuming that the images of the Hankel transform belong to this space or to the weighted Lebesgue space on the positive half axis the Paley-Wiener theorems give a correspondence of them to continuous or integrable functions which vanish in some infinite interval.
scientific article; zbMATH DE number 792944
scientific article