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Multiresolution analysis and multivariate approximation of smooth signals in \(C_ B(\mathbb{R}^ d)\). (English) Zbl 0887.42030

Summary: In this paper we derive rates of approximation for a class of linear operators on \(C_B(\mathbb{R}^d)\) associated with a multiresolution analysis \(\{V_n\}_{n\in\mathbb{Z}}\). We show that for a uniformly bounded sequence of linear operators \(\{T_n\}_{n\in\mathbb{Z}}\) satisfying \(T_nf\equiv f\) on the subspace \(V_n\cap C_B(\mathbb{R}^d)\), a lower bound for the approximation order is determined by the number of vanishing moments of a prewavelet set. We consider applications to extensions of generalized projection operators as well as to sampling series.

MSC:

42C15 General harmonic expansions, frames
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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