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2012 | OriginalPaper | Buchkapitel
Multiple Subdivision Schemes
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Motivated by the concept of directionally adapted subdivision for the definition of shearlet multiresolution, the paper considers a generalized class of multivariate stationary subdivision schemes, where in each iteration step a scheme and a dilation matrix can be chosen from a given finite set. The standard questions of convergence and refinability will be answered as well as the continuous dependence of the resulting limit functions from the selection process. In addition, the concept of a
canonical factor
for multivariate subdivision schemes is introduced, which follows in a straightforward fashion from algebraic properties of the scaling matrix and takes the role of a smoothing factor for symbols.