A characterization of the inverse Radon transform associated with the classical domain of type one

Abstract

Let D(Ω, Φ) be the unbounded realization of the classical domain of type one. In general, its Šilov boundary is a nilpotent Lie group of step two. In this article, we characterize a subspace of (Schwartz space) on which the Radon transform is a bijection and give another characterization for this subspace . Also, we show that the two characterizations are equivalent. Finally, we give an inversion formula of the Radon transform on by using continuous wavelet transform.