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INVERSION OF THE RADON TRANSFORM ASSOCIATED WITH THE CLASSICAL DOMAIN OF TYPE ONE

Department of Mathematics, School of Mathematics and Information Sciences, Guihuagang Campus, Guangzhou University, Guangzhou 510405, P. R. China

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HEPING LIU

LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, P. R. China

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https://doi.org/10.1142/S0129167X05003120Cited by:8 (Source: Crossref)

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 define the Radon transform on , and obtain an inversion formula in terms of a determinantal differential operator. Moreover, we characterize a subspace of on which the Radon transform is a bijection. By use of the suitable continuous wavelet transform we establish a new inversion formula of the Radon transform in weak sense without the assumption of differentiability.

Keywords:

AMSC: 43A85, 44A15

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