Paley-Wiener-type theorems for the Hankel transform of positive half-integer order in weighted $L^2$-spaces

In this paper, we obtain several analogues of the Paley-Wiener theorem for the Hankel transform of order $m+1/2$ with $m\in\mathbb N$ in weighted spaces $L^2((0;1);x^{2m} dx)$. These Paley-Wiener-type theorems describe a certain class of odd entire functions of exponential type $\sigma \leqslant 1$ 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.