张量积空间中框架的一种新构造

A New Construction of Frames in the Tensor Product Space

因为非张量积且较实用的高维小波基不多见,常常用低维的小波基作张量积来构造高维小波基。本文中,我们利用算子论的方法,研究了两个Hilbert空间中的框架张量以及张量积空间中框架的关系。将高维空间中的框架表示可以转化为低维空间中的框架张量,同时也可以把高维空间中的向量用低维空间的框架张量来表示。

In the wavelet analysis,we rarely see non-tensor product and high-dimensional wavelet bases,we always construct high-dimensional wavelet base by using low-dimensional ones.In this paper,it is studied that the relations between tensor product of frames in two Hilbert spaces and frames in a tensor product space by using operator theory.We convert frames in a high-dimensional space into a tensor of frames in some low-dimensional spaces,and represent vectors in a high-dimensional space as the tensor of frames in some low-dimensional spaces.