Admissible wavelets and inverse radon transofrm associated with the affine homogeneous Siegel domains of type II

Let D(Ω,Φ) be the affine homogeneous Siegel domain of type II, whose Silov boundary N is a nilpotent Lie group of step two. In this article, we develop the theory of wavelet analysis on N . By selecting a set of mutual orthogonal wavelets we give a direct sum decomposition of L2(D(Ω,Φ)), the first component A0,0 of which is the Bergman space. Moreover, we study the Radon transform on N , and obtain an inversion formula R−1 = (π)−2dLRL which is an extension of that by Strichartz [R. S. Strichartz, L harmonic analysis and Radon transforms on the Heisenberg group, J. Funct. Anal. 96 (1991), 350–406.]. We devise a subspace of L2(N) on which the Radon transform is a bijection. Using wavelet inverse transform, we establish an inversion formula of the Radon transform in the weak sense.

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