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Refinable function vectors. (English) Zbl 0913.42028

Dependence of properties of refinable function vectors on their refinement masks is studied. In particular, necessary and sufficient conditions for the convergence of cascade algorithms, for the stability and orthonormality of refinable vectors are found. An estimate of regularity of refinable functions in terms of number of vanishing moments of the refinement mask is given.

MSC:

42C15 General harmonic expansions, frames
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
41A15 Spline approximation
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