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乘积Laguerre超群上的广义小波变换及Radon逆变换
Generalized Wavelets and Inversion of the Radon Transform on the Product Laguerre Hypergroup
【作者】 刘沛;
【导师】 何建勋;
【作者基本信息】 广州大学 , 应用数学, 2007, 硕士
【摘要】 令H1是3-维的海森堡群, H1上径向函数空间的基础流形记为[0,+∞)×R,称为Laguerre超群([25]).自然地, Kn = [0,+∞)n×Rn称为乘积Laguerre超群.本文首先建立了Kn = [0,+∞)n×Rn上的平移算子和L2(Kn,dμ)上的Plancherel公式.其次,讨论Kn = [0,+∞)n×Rn上的广义小波变换和Radon变换理论.然后,我们构造S(Kn)(施瓦茨空间)的一个特征子空间SR(Kn),指出Radon变换在SR(Kn)上是一一映射,并给出与SR(Kn)等价的S(Kn)的另一个特征子空间S?,2(Kn).最后,在弱意义下,利用广义小波逆变换得到Kn = [0,+∞)n×Rn上Radon变换的逆公式.类似地,此结果在海森堡群上成立.
【Abstract】 Let H1 be the 3-dimensional Heisenberg group. The fundamental manifold ofthe radial function space for H1 can be denoted by [0, +∞)×R, which is just theLaguerre hypergroup(see[25]). Naturally, K~n = [0, +∞)~n×R~n is product Laguerrehypergroup. In this paper, we construct a generalized translation operator on K~n =[0,+∞)~n×R~n, and establish the Plancherel formula on L2(K~n,dμ). Then we discussthe continuous wavelets transform and Radon transform on K~n, and we characterizea subspace SR(K~n) of S (K~n)(Schwartz space), on which Radon transform is abijection. Also, we give another characterized subspace S?,2(K~n) which is equivalentto SR(K~n). Using the inverse wavelet transform, we obtain an inversion formulaof Radon transform on K~n in the weak sense. Analogously, the same case can beextended to the Heisenberg group.
【Key words】 Radon transform; Generalized wavelets; Heisenberg group; Laguerre hypergroup; Plancherel formula;
- 【网络出版投稿人】 广州大学 【网络出版年期】2007年 06期
- 【分类号】O177.91
- 【下载频次】80