Abstract
In wavelet theory smootheness is one of the main interests. By the Mallat-Meyer construction (see [He] or [Me]) the problem of finding smooth wavelets is reduces to finding smooth scaling functions of multiresolutions. From a given scaling function g a smoother one can be made by taking convolution with e. g. the characteristic function of [0,1]. In this article a characterisation of the multiresolution generated by that convolution-will be given by means of primitives of functions in the multiresolution generated by g. From this, the spline multiresolutions follow as a special case.
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van Gaans, O. Multiresolutions and primitives. Approx. Theory & its Appl. 13, 49–56 (1997). https://doi.org/10.1007/BF02836259
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DOI: https://doi.org/10.1007/BF02836259