【摘 要】
：
Let F(2n,2)be the free nilpotent Lie group of step two on 2n generators,and let P denote the affine automorphism group of F(2n,2).In this article the theory of
【机 构】
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GuangzhouUniversity
【出 处】
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Harmonic Analysis and Applications(2014调和分析及其应用学术会议)
论文部分内容阅读
Let F(2n,2)be the free nilpotent Lie group of step two on 2n generators,and let P denote the affine automorphism group of F(2n,2).In this article the theory of continuous wavelet transform on F(2n,2)associated with P is developed,and then a type of radial wavelet is constructed.Secondly,the Radon transform on F(2n,2)is studied,and two equivalent characterizations of the range for Radon transform are given.Several kinds of inversion Radon transform formulae are established.One is obtained from the Euclidean Fourier transform;the others are from the group Fourier transform.By using wavelet transforms we deduce an inversion formula of the Radon transform,which does not require the smoothness of functions if the wavelet satisfies the differentiability property.In particular,if n = 1,F(2,2)is the 3-dimensional Heisenberg group H1,the inversion formula of the Radon transform is valid,which is associated with the sub-Laplacian on F(2,2).This result cannot be extended to the case n ＞ 1.
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