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Radon transforms on Siegel-type nilpotent Lie groups

Authors:	Xingya FAN Jianxun HE Jinsen XIAO Wenjun YUAN

Affiliation:	¹. School of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China². School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China³. School of Sciences, Guangdong University of Petrochemical Technology, Maoming 525000, China

Abstract:	Let $N$ := $H n × ℂ n$ be the Siegel-type nilpotent group, which can be identified as the Shilov boundary of Siegel domain of type II, where $H n$ denotes the set of all $n × n$ Hermitian matrices. In this article, we use singular convolution operators to define Radon transform on $N$ and obtain the inversion formulas of Radon transforms. Moveover, we show that Radon transform on $N$ is a unitary operator from Sobolev space Wⁿ^;2 into L²( $N$ ):

Keywords:	Siegel domain Siegel-type nilpotent group Fourier transform Radon transform

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