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An estimate for multivariate interpolation. (English) Zbl 0558.41008

An estimate of the \(L^ p=L^ p(R^ n)\) norm of a function is given in terms of its values on a (not necessarily regular) grid of points and the \(L^ p\) norms of its k-th order derivatives, \(kp>n\). The result is useful in obtaining estimates for multivariate interpolation schemes; this is illustrated by an example involving generalized splines.

MSC:

41A05 Interpolation in approximation theory
41A17 Inequalities in approximation (Bernstein, Jackson, Nikol’skiĭ-type inequalities)
41A63 Multidimensional problems
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References:

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