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On compactly supported spline wavelets and a duality principle. (English) Zbl 0759.41008
The authors consider a multiresolution analysis of $$L^ 2(\mathbb{R})$$ generated by the $$m$$-th order $$B$$-spline $$N_ m(x)$$. Then they describe the wavelet subspaces $$W_ k$$ and construct a basic spline-wavelet with compact support that generates $$W_ k$$. By Fourier transform techniques one can handle the corresponding pair of two-scale relations and a decomposition formula. Here the main idea is a duality principle which states that the pair of two-scale relations can be used as the decomposition formula, and vice versa. This approach yields a very desirable decomposition of every $$L^ 2$$-function into a direct sum of compactly supported spline wavelets.

##### MSC:
 41A15 Spline approximation 42C05 Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis 41A05 Interpolation in approximation theory 41A30 Approximation by other special function classes
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##### References:
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