Abstract
Suppose that η1, ..., ηn are measurable functions in L2(ℝ). We call the n-tuple (η1, ..., ηn) a Parseval super frame wavelet of length n if $$\left\{ {2^{\tfrac{k} {2}} \eta _1 \left( {2^k t - \ell } \right) \oplus \cdots \oplus 2^{\tfrac{k} {2}} \eta _n \left( {2^k t - \ell } \right):k,\ell \in \mathbb{Z}} \right\}$$ 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.
Published Version
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