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An extension of a bound for functions in Sobolev spaces, with applications to \((m, s)\)-spline interpolation and smoothing. (English) Zbl 1221.41012
Let \(X\) be an open subset of \(\mathbb R^n\) that has a Lipschitz- continuous boundary. The authors improve and extend to a bigger class of functions a Sobolev-bound obtained by interpolation for functions defined on \(X\). The authors techniques include proving two Sobolev embedding theorems and introducing a “random noise” hypothesis.

MSC:
41A25 Rate of convergence, degree of approximation
41A05 Interpolation in approximation theory
41A15 Spline approximation
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