Abstract
Generalized cardinal B-splines are defined as convolution products of characteristic functions of self-affine lattice tiles with respect to a given integer scaling matrix. By construction, these generalized splines are refinable functions with respect to the scaling matrix and therefore they can be used to define a multiresolution analysis and to construct a wavelet basis. In this paper, we study the stability and linear independence properties of the integer translates of these generalized spline functions. Moreover, we give a characterization of the scaling matrices to which the construction of the generalized spline functions can be applied.
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Communicated by Ronald A. DeVore.
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Dahlke, S., Latour, V. & Neeb, M. Generalized cardinal B-splines: Stability, linear independence, and appropriate scaling matrices. Constr. Approx 13, 29–56 (1997). https://doi.org/10.1007/BF02678429
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DOI: https://doi.org/10.1007/BF02678429