Sauer, Thomas Stationary vector subdivision: quotient ideals, differences and approximation power. (English) Zbl 1057.42029 RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 96, No. 2, 257-277 (2002). The stationary vector subdivision operator \( S_A = S_{M,A} \) based on an expanding matrix \( M\in \mathbb Z^{s\times s} \) and a finitely supported matrix valued mask \( A \in l_p^{N \times N}(\mathbb Z^s) \) is defined for any \( c \in l^N_p (\mathbb Z )\) by \[ S_{M,A} c := A \star_M c := \sum_{\beta \in \mathbb Z^s}A(\cdot - M \beta) c(\beta) . \] In this paper, those subdivision schemes which possess polynomial eigensequences are characterized in terms of a difference operator. Moreover, convergent stationary subdivision schemes are connected to a factorization property which is expressed in terms of quotient ideals. These results can be applied in order to describe whether a subdivision operator \( S_A\) preserves polynomial sequences of a certain total degree. Reviewer: Gerlind Plonka (Duisburg) Cited in 11 Documents MSC: 42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems Keywords:stationary subdivision; difference operators; quotient ideals; refinable functions PDFBibTeX XMLCite \textit{T. Sauer}, RACSAM, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat. 96, No. 2, 257--277 (2002; Zbl 1057.42029) Full Text: EuDML