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...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.展开更多
基金Supported by the National Natural Science Foundation of China(11071065,11101142,11171306,10671062)the China Postdoctoral Science Foundation(20100480942)+1 种基金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
文摘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.