Han, Bin; Mo, Qun Multiwavelet frames from refinable function vectors. (English) Zbl 1059.42030 Adv. Comput. Math. 18, No. 2-4, 211-245 (2003). A \(d\)-refinable function vector \(\phi = (\phi_1, \ldots, \phi_r)^T\) satisfies the refinement equation \[ \phi = | d| \sum_{k \in {\mathbb Z}} a_k \phi(d\cdot - k), \] where \(r\) is the multiplicity, \(d\) the dilation factor, and \(a\) is the finitely supported sequence of \(r\times r\) matrices. Such a vector generates a wavelet function vector by \[ \widehat \psi^l (d \xi) = b^l(\xi) \widehat \phi(\xi), \] where \(l=1, \ldots, L\) and \(b^l\) are periodic trigonometric polynomials.The paper under review studies the properties of dual wavelet frames and of wavelet frames generated by refinable function vectors. In particular, algorithms for constructing dual wavelet frames with maximum vanishing moments are given. Moreover, symmetry/antisymmetry properties of wavelets are examined and examples are provided. Reviewer: Wojciech Czaja (Wien) Cited in 45 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems 42C15 General harmonic expansions, frames Keywords:dual wavelet frames; wavelet frames; refinable function vectors; multiwavelets; refinable Hermite interpolants; sum rules; vanishing moments; symmetry × Cite Format Result Cite Review PDF Full Text: DOI