Andrew Vogt

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Quantitative bounds on rates of approximation by linear combinations of Heaviside plane waves are obtained for sufficiently differentiable functions f which vanish rapidly enough at infinity: for d odd and f ∈ C d (R d), with lower-order partials vanishing at infinity and dth-order partials vanishing as x −(d+1+ε) , ε > 0, on any domain ⊂ R d with unit(More)
It is shown that for any positive integer n and any function in Lp([0, 1] d) with p ∈ [1, ∞) there exists a best approximation by linear combinations of n characteristic functions of half-spaces. Further, sequences of such linear combinations converging in distance to the best approximation distance have subsequences converging to the best approximation,(More)
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