【作者】 温丽群；

【导师】 何建勋；

【作者基本信息】 广州大学 ， 基础数学， 2010， 硕士

【摘要】 令H1是3-维的海森堡群,称Hn1 = H1×H1×...×H1为乘积海森堡群.本文讨论乘积海森堡群上的广义小波变换,利用小波变换的反演公式得到了Radon变换的逆公式.其次,结合小波变换研究了魏尔变换的有界性.全文共分为三章:第一章,介绍本文的学术背景.第二章,研究了乘积海森堡群上与Schro¨dinger表示相应的傅里叶变换以及小波变换,并利用小波变换的反演公式得到Radon变换的逆公式.第三章,研究了乘积海森堡群上与Bargmann-Fock表示相应的傅里叶变换以及小波变换的性质,并讨论与小波变换联系的魏尔变换的有界性.更多还原

【Abstract】 Let H1 be the real 3-diemensional Heisenberg group, then we call Hn1 = H1×H1×...×H1 the product Heisenberg group. In this article, we first discuss thegeneralized wavelet transform of the product Heisenberg group, and use the inversewavelet transform to get an inversion formula of Radon transform. In addition, westudy the boundedness of Weyl transform associated with the wavelet transform. Itconsists of 3 chapters:In Chapter 1, the academic background is introduced.In Chapter 2, we study the Fourier transform defined by Schro¨dinger representa-tions and construct the wavelet transform on the product Heisenberg group. Moreover,we obtain an inversion formula of Radon transform by using the inverse wavelet trans-form.In Chapter 3, we study the Fourier transform related to the Bargmann-Fock rep-resentations and the wavelet transform on the product Heisenberg group. Furthermore,we investigate the boundedness of Weyl transform associated with the wavelet trans-form.更多还原