An analogue of the Paley-Wiener theorem for the Hankel type transform in weighted L2-spaces

Abstract

In this paper, we establish some analogues of the Paley-Wiener theorem for the Hankel type transform of half-integer order less than -1 in weighted L²-spaces. These Paley-Wiener-type theorems gives a description of the class of even entire functions of exponential type σ ≤ 1 under this transformation in terms of solutions from the corresponding spaces of some differential equations.