半直线伸缩调制框架集  

The Dilation-and-Modulation Frame Sets on the Half Real Line

作　　者：李云章[1] 王雅慧 Yun Zhang LI;Ya Hui WANG(College of Applied Sciences,Beijing University of Technology,Beijing 100124,P.R.China)

机构地区：[1]北京工业大学应用数理学院

出　　处：《数学学报（中文版）》2020年第1期45-60,共16页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11971043)

摘　　要：本文研究右半直线平方可积函数空间L^2(R+)中的一类伸缩调制系.实际问题中时间变量不可取负值,L^2(R+)可模拟因果信号空间.但因R+按加法不能作成一个群,它不容许小波与Gabor系.我们研究L^2(R+)中由特征函数生成的伸缩调制系(MD-系)框架,引入了R+中MD-框架集的概念,利用"伸缩等价"与"基数函数"方法刻画了L^2(R+)中MD-Bessel集与完备集;得到了关于MD-Riesz基集的两个充分条件,并证明了通过对MD-Riesz基集进行有限可测分解可得到MD-框架集.This paper addresses a class of dilation-and-modulation(MD) systems in the space L^2(R+) of square integrable functions defined on the right half real line R+.In practice,the time variable cannot be negative.L2(R+) models the causal signal space,but it admits no wavelet and Gabor systems due to R+being not a group under addition.We study the dilation-and-modulation systems in L^2(R+) generated by characteristic functions.We introduce the notion of frame sets in R+.Using "dilation-equivalence" and "cardinality function" methods we characterize MD-Bessel and complete sets;obtain two sufficient conditions for MD-Riesz basis sets;and prove that an arbitrary finite and measurable decomposition of an MD-Riesz basis set leads to an MD-frame set.

关 键 词：伸缩调制系 框架 RIESZ基 

分 类 号：O174.2[理学—数学]