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

R.V. Khats'

doi:10.15421/242526

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

R.V. Khats' (Drohobych Ivan Franko State Pedagogical University), https://orcid.org/0000-0001-9905-5447

Abstract

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.

Keywords

Paley-Wiener theorem; Hankel transform; Bessel function; Fubini's theorem; entire function of exponential type; half-integer order; weighted space

MSC 2020

Pri 33C10, Sec 44A15, 46E30, 30D10, 46F12

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References

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