基于全纯小波的多分辨分析

Multiresolution Analysis On Holomorphic Wavelets

首先考虑四元数上半平面的边界在特殊线性群SL(2,C)的子群作用下的酉表示。其次利用投影算子将L^2(R^2)投影到广义上半平面T_Γ上的全纯函数空间H^2(T_Γ)及其共轭空间H^2(T_Γ)上。由L^2(R^2)的多分辨分析,可获得这两个投影空间的多分辨分析,从而解决L^2(R^2)的直和分解问题。

In this paper,the author firstly considers the unitary representation on the boundary of the quaternionic upper half plane under the subgroup of SL（2,C）. By using projection operator,we project the L^2（R^2） onto H-2（ TΓ） and its conjugate space H^2（ T^-Γ）respectively,where H-2（ TΓ） is the set of all holomorphic functions on the generalized upper half plane TΓWe also obtain the multiresolution analysis of the two projected space above via the multiresolution analysis of L^2（R^2）,and finally we have the direct sum decomposition for L^2（R^2）.