## 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

### Keywords:

Sobolov; Interpolation; Splines; Smoothing
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