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Fractal functions and wavelet expansions based on several scaling functions. (English) Zbl 0806.41016
Using fractal functions the authors present a method for constructing translation and dilation invariant function spaces. Necessary and sufficient for these spaces to form a multiresolution analysis of \(L^ 2(\mathbb{R})\) are given. Two examples are included.

MSC:
41A30 Approximation by other special function classes
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
41A15 Spline approximation
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