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

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.