Geodesic
Smoothing of functions in finite-dimensional Banach spaces
Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 207-223.

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We consider the problem of the linear smoothing of continuous functions defined on the unit ball in $\mathbb R^n$, and look for lower bounds for the norms of the derivatives of the approximating functions on the unit balls in arbitrary finite-dimensional spaces. 
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     title = {Smoothing of functions in finite-dimensional {Banach} spaces},
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I. G. Tsar'kov. Smoothing of functions in finite-dimensional Banach spaces. Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 207-223. http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a8/

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