On Parseval super-frame wavelets

摘要

Suppose that η_1,...,η_n are measurable functions in L^2(R).We call the n-tuple(η_1,...,η_n) a Parseval super frame wavelet of length n if {2^(k/2) η_1(2~kt-l) ⊕···⊕2^(k/2) η_n(2~kt-l):k,l∈Z} is a Parseval frame for L^2(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.