Intrinsic \(s\)-elementary Parseval frame multiwavelets in \(L^2(\mathbb R^d)\)
This paper studies some interesting theoretical properties of Parseval frame multiwavelets and addresses two problems on Parseval frame multiwavelets. Let \(A\) be a real expansive dilation matrix and \(m\) be a positive integer. Theorem 3.4 shows that there always exists an intrinsic \(A\)-dilation Parseval frame multiwavelet set with length \(m\) (see Definition 1.1). Theorem 4.1 proves that the set of all \(A\)-dilation s-elementary Parseval frame multiwavelets of length \(m\) is path-connected and Theorem 4.5 demonstrates that the set of all intrinsic \(A\)-dilation s-elementary Parseval frame multiwavelets of length \(m\) is path-connected. Furthermore, a generalized result in Theorem 5.2 shows that there exist intrinsic \(A\)-dilation Parseval frame multiwavelets of length \(m\).
s-elementary Parseval frame multiwavelets
scientific article; zbMATH DE number 5706233