Tight frame wavelets, their dimension functions, MRA tight frame wavelets and connectivity properties
This is a continuation of the study of generalized low pass filters and MRA frame wavelets initiated by the authors in [J. Geom. Anal. 11, 311-342 (2001; Zbl 0985.42020)]. This first paper focused on the construction of such functions. Here, the authors are particularly interested in the role played by the dimension function. In particular, they characterize all semi--orthogonal Tight Frame Wavelets (TFW) by showing that they correspond precisely to those for which the dimension function is nonnegative and integer valued. They also show that a TFW arises from their MRA construction if and only if the dimension of a particular linear space is either zero or one, and present several examples. In addition, the authors study the class of \textit{MSF tight frame wavelets}, which are those TFWs \(\psi\) for which \(|\widehat{\psi}|\) attains only the values 0 and 1, and obtain a result concerning their connectivity.
scientific article; zbMATH DE number 1896706