On Parseval super-frame wavelets  

作　　者：LI Zhong-yan SHI Xian-liang 

机构地区：[1]College of Mathematics and Computer Science,Key Laboratory of High Performance Computing and Stochastic Information Processing(HPCSIP)(Ministry of Education of China),Hunan Normal University,Changsha 410081,China [2]Department of Mathematics and Physics,North China Electric Power University,Beijing 102206,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2012年第2期192-204,共13页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China(11071065,11101142,11171306,10671062);the China Postdoctoral Science Foundation(20100480942);the Ph.D.Programs Foundation of the Ministry of Education of China(20094306110004);the Program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province

摘　　要：Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l∈Z} is a Parseval frame for L2（R）⊕n.In high dimensional case,there exists a similar notion of Parseval super frame wavelet with some expansive dilation matrix.In this paper,we will study the Parseval super frame wavelets of length n,and will focus on the path-connectedness of the set of all s-elementary Parseval super frame wavelets in one-dimensional and high dimensional cases.We will prove the corresponding path-connectedness theorems.Suppose that η1,...,η_n are measurable functions in L2（R）.We call the n-tuple（η1,...,ηn） a Parseval super frame wavelet of length n if {2^（k/2） η1（2~kt-l） ⊕···⊕2^（k/2） ηn（2kt-l）：k,l∈Z} is a Parseval frame for L2（R）⊕n.In high dimensional case,there exists a similar notion of Parseval super frame wavelet with some expansive dilation matrix.In this paper,we will study the Parseval super frame wavelets of length n,and will focus on the path-connectedness of the set of all s-elementary Parseval super frame wavelets in one-dimensional and high dimensional cases.We will prove the corresponding path-connectedness theorems.

关 键 词：Parseval frame wavelet super frame s-elementary Parseval super frame wavelet. 

分 类 号：O174.2[理学—数学] V474.25[理学—基础数学]