Paley-Wiener-type theorems for the Hankel transform of positive half-integer order in weighted L2-spaces

Abstract

In this paper, we obtain several analogues of the Paley-Wiener theorem for the Hankel transform of order m+1/2 with m∈N in weighted spaces L2((0;1);x2m dx). These Paley-Wiener-type theorems describe a certain class of odd entire functions of exponential type σ≤1 under this transformation and provide methods to constructing such a kind of Hankel transforms in terms of solutions from the corresponding spaces of some differential equations.