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Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets. (English) Zbl 0932.42021
Using orthogonal polynomials (i.e., ultraspherical polynomials), the authors construct families of C 0 and C 1 orthogonal, compactly supported spline multiwavelets of L 2 () with various approximation orders. In the case of symmetric or antisymmetric multiscaling functions, this method allows the construction of symmetric or antisymmetric multiwavelets. By restriction on [0,1], these results yield C 0 and C 1 spline multiwavelet bases of L 2 [0,1]. A C 2 compactly supported spline multiwavelet basis of L 2 () is also sketched, but the formulas become very complicated.
MSC:
42C40Wavelets and other special systems
41A15Spline approximation
33C55Spherical harmonics