有限维Hilbert空间中等模紧框架的一类构造方法

A class of methods for constructing equal-norm tight frames in a finite dimensional Hilbert space

利用H_n中已有的等模紧框架构造H_(n+1)中的等模紧框架;并利用H-_n中已有的紧框架来构造H_(n+1)中的Parseval框架.最后给出了在这种方法下构造R^n中框架元素个数为n+1的比较稀疏的单位模紧框架的具体表达式.

We use the existing equal-norm tight frames for Hn to construct equal-norm tight frames for Hn＋1. We also use the existing tight frames for Hn to construct Parseval frames for Hn＋1. In addition, we give a detailed expression of sparse unit-norm tight frames with n＋1 vectors for Rn in this construction.