调和框架的基本素紧分解及其应用

Elementary Prime Tight Decomposion of Harmonic Frames and Their Applications

本文提出了基本素紧框架的概念,证明任意阶调和框架都可由基本素紧框架的并、直和与张量积的投影得到.反之,基本素紧框架的混合运算未必为调和框架,但却生成更一般的等范紧框架,这为构造等范紧框架提供了一种新的方法.最后,本文研究了几种新构造的等范紧框架,得出一些较原框架更好的性质.

This paper puts forward the conception of elementary prime tight frames, proving that any finite dimension harmonic frames can be decomposed as unions, direct sums and projection of tensor products of those frames. Conversely, the compound of elementary prime tight frames may not be a harmonic frame, but becomes a general equal normal tight frame （ENTF）, which provides a novel method to construct ENTF. Finally, some kinds of ENTF are studied, which have better properties as compared with the former frames.