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

Key Points

• The aim is to obtain analogues of the Paley-Wiener theorem for the Hankel transform of positive half-integer order.
• Investigated Hankel transforms of order m+1/2 in weighted spaces L^2
• Analyzed odd entire functions of exponential type
• Constructed Hankel transforms using solutions of differential equations
• Described properties of a class of odd entire functions under the Hankel transform
• Provided methods for constructing Hankel transforms
• Established relationships with solutions of corresponding differential equations