连续小波型编织框架及其性质

Continuous Wavelet Weaving Frames and Their Properties

Hilbert空间中连续小波型编织框架是连续小波型框架和编织框架的推广.在已有文献的基础上,研究了Hilbert空间中连续小波型编织框架的构造及其相关性质.通过有界线性算子构造连续小波型编织框架并讨论了自身结构的一些性质;探究了连续小波型框架算子的范数与编织框架之间的关系;借助分析算子得到了连续小波型编织框架与连续编织框架之间的一个充要条件;最后证明了连续小波型编织框架在数列扰动下的稳定性.

The continuous wavelet weaving frame in Hilbert space is a generalisation of the continuous wavelet frame and the weaving frame.In this paper,based on the existing literature,we study the construction of continuous wavelet weaving frames in Hilbert spaces and their related properties.The continuous wavelet weaving frame is constructed by means of a bounded linear operator and some properties of its own structure are discussed;the relationship between the parametrization of the continuous wavelet frame operator and the weaving frame is investigated;a suficient condition between the continuous wavelet weaving frame and the continuous weaving frame is obtained with the help of analytic operators;and finally,the stability of the continuous wavelet weaving frame is proved under the perturbation of the series.