Generalized cardinal B-splines: Stability, linear independence, and appropriate scaling matrices |
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Authors: | S Dahlke V Latour M Neeb |
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Institution: | (1) Institut für Geometrie und Praktische Mathematik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany |
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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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Keywords: | AMS classification" target="_blank">AMS classification 41A15 41A30 41A63 |
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