摘要
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).
作者
丁凯
DING Kai(School of Mathematics and Information Sciences,Guangzhou University,Guangzhou 510006,China)
出处
《广东石油化工学院学报》
2018年第4期76-81,共6页
Journal of Guangdong University of Petrochemical Technology
基金
国家自然科学基金(11671414
11471040)
关键词
四元数上半平面
酉表示
全纯函数空间
多分辨分析
Quaternionic upper half plane
Unitary- representation
The space of holomorphic functions
Multiresolution analysis