Approximation by linear combinations of translates of a single function

2020/12/15 by Dũng, Dinh, Huy, Vu Nhat
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2012.08086

Abstract

We study approximation by arbitrary linear combinations of n translates of a single function of periodic functions. We construct some linear methods of this approximation for univariate functions in the class induced by the convolution with a single function, and prove upper bounds of the L^p-approximation convergence rate by these methods, when n → ∞, for 1 ≤ p ≤ ∞. We also generalize these results to classes of multivariate functions defined the convolution with the tensor product of a single function. In the case p=2, for this class, we also prove a lower bound of the quantity characterizing best approximation of by arbitrary linear combinations of n translates of arbitrary function.

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