Summary
In this paper, we develop a framework suitable for performing a multiresolution analysis using univariate spline spaces of arbitrary degree and with non-uniform knot-sequences. To this end, we show, among other things, the existence of compactly supported prewavelets and of prewavelets that are globally supported, but decay exponentially. In each case we obtain a decomposition of a fine spline space as a sum of a coarse spline space plus a spline space spanned by prewavelets.
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Buhmann, M.D., Micchelli, C.A. Spline prewavelets for non-uniform knots. Numer. Math. 61, 455–474 (1992). https://doi.org/10.1007/BF01385520
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DOI: https://doi.org/10.1007/BF01385520