On finite Hankel transformation of generalized functions

Abstract

In this paper the finite Hankel transformation of generalized function of a certain space is defined, and an inversion formula for the transformation is established. The inversion formula gives rise to a Fourier-Bessel series expansion of generalized functions. The convergence of the series is interpreted in the weak distributional sense. An operation transform formula is also obtained, which together with the inversion formula, is applied in solving certain distributional differential equations.