On Parseval super-frame wavelets

Suppose that η,...,ηare measurable functions in L~2(R).We call the n-tuple(η,...,η) a Parseval super frame wavelet of length n if {2η(2~kt-l) ⊕···⊕2η(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.