Wavelet transform and radon transform on the quaternion Heisenberg group

被引：0
作者：
Jian Xun He
He Ping Liu
机构：
[1] Guangzhou University,School of Mathematics and Information Sciences
[2] Guangzhou University,Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes
[3] Peking University,LMAM, School of Mathematical Sciences
来源：
Acta Mathematica Sinica, English Series | 2014年 / 30卷
关键词：
Quaternion Heisenberg group; wavelet transform; Radon transform; inverse Radon transform; 43A80; 44A12;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Let [inline-graphic not available: see fulltext] be the quaternion Heisenberg group, and let P be the affine automorphism group of [inline-graphic not available: see fulltext]. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of P on [inline-graphic not available: see fulltext]. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on [inline-graphic not available: see fulltext]. A Semyanistyi-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on [inline-graphic not available: see fulltext] both by the Euclidean Fourier transform and the group Fourier transform. These two treatments are essentially equivalent. We also give an inversion formula by using wavelets, which does not require the smoothness of functions if the wavelet is smooth. In addition, we obtain an inversion formula of the Radon transform associated with the sub-Laplacian on [inline-graphic not available: see fulltext].
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页码：619 / 636
页数：17
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