摘要
首先研究两类Shearlet群N_((d,s))和H_d(d=1,2,3)的结构,给出N_((d,s))和H_d的同构群,同时给出了N_((d,s))和H_d上的自同构群.接着利用群直积方法,构造高阶群.在此基础上,给出L^2(R^3)上的酉算子与对应Shearlet群和高阶群之间的关系,同时给出了满足Parseval等式时函数f∈L^2(R^3)在群表示意义下的展开式.最后利用两类不完全拟Beta函数给出L^2(R^3)上修波的具体构造.
The structure of two sort of Shearlet groups N（d,s） and Hd（d = 1,2,3） is first investigated in this paper,and the isomorphic and automorphic groups for N（d,s）and H_d are discussed.Next,by methods of group product,higher order groups are constructed.Henceforth,the corresponding relationship between unitary operators in L^2（R^3） and associated Shearlet groups and higher order groups are constructed,and some function f ∈ L^2（R^3） satisfied with the Parseval identity is developed underlying the spirit of group representation.Finally,concrete examples of shearlets in L^2（R^3）is constructed by utilizing two kind of incomplete quasi-beta functions.
出处
《系统科学与数学》
CSCD
北大核心
2016年第1期107-114,共8页
Journal of Systems Science and Mathematical Sciences
关键词
群表示
修波构造
不完全拟Beta函数
Group representation
construction of Shearlets
incomplete quasi-beta functions
