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Zbl 0932.42021
Donovan, G.C.; Geronimo, J.S.; Hardin, D.P.
Orthogonal polynomials and the construction of piecewise polynomial smooth wavelets. (English)
[J] SIAM J. Math. Anal. 30, No.5, 1029-1056 (1999). ISSN 0036-1410; ISSN 1095-7154/e

Using orthogonal polynomials (i.e., ultraspherical polynomials), the authors construct families of $C^0$ and $C^1$ orthogonal, compactly supported spline multiwavelets of $L^2(\bbfR)$ 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 $L^2(\bbfR)$ is also sketched, but the formulas become very complicated.
[M.Tasche (Rostock)]

MSC 2000:: *42C40 Wavelets
41A15 Spline approximation
33C55 Elliptic integrals as hypergeometric functions

Keywords: piecewise polynomial smooth multiwavelets; orthogonal polynomials; ultraspherical polynomials; spline multiwavelets; multiscaling

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