仿射框架的必要条件  

Necessary Condition of the Affine Frames with Composite Dilations

作　　者：陈洁[1] Chen Jie(School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201 ,China)

机构地区：[1]湖南科技大学数学与计算科学学院

出　　处：《湖南科技大学学报（自然科学版）》2018年第3期109-117,共9页Journal of Hunan University of Science And Technology：Natural Science Edition

基　　金：湖南省教育厅一般资助项目(16C0634)

摘　　要：在函数空间中,基的限制条件比较严格,通常情况下,框架可以很好地替代基的作用,所以框架的相关研究具有较大的实际意义.对于框架的必要条件的研究已经有不少成果,对于高维情况的研究是其中的一个重要推广.在框架定义的和式中,通过改变求和的方式,引入A进求和法,研究和式的收敛情况.选择特定的函数满足框架的定义,从而获得带有膨胀矩阵及旋转矩阵的仿射框架的必要条件.In the function space,the limited condition of the base is strict.The affine frame can replace the role of the base. The related research of frame has great practical significance. There are a lot of achievements about the necessary conditions of the frame. The study of frame in N dimension is a important promotion. In the summation of the frame definition,changing the summation way and using the A-adic vector summation method,research the convergence of the summation formulas. Choose the specific function to satisfy the definition of the frame,by which the necessary condition of the affine frames is abtained,which is of dilatation matrix and rotation matrix.

关 键 词：仿射框架 必要条件 膨胀矩阵 旋转矩阵 

分 类 号：O174.2[理学—数学]