Geodesic
Extending Peano derivatives
Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 387-406.

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Let $H\subset [0,1]$ be a closed set, $k$ a positive integer and $f$ a function defined on $H$ so that the $k$-th Peano derivative relative to $H$ exists. The major result of this paper is that if $H$ has finite Denjoy index, then $f$ has an extension, $F$, to $[0,1]$ which is $k$ times Peano differentiable on $[0,1]$ with $f_i=F_i$ on $H$ for $i=1,2,\ldots,k$.
DOI : 10.21136/MB.1994.126113
Classification : 26A24
Keywords: Peano derivatives; Denjoy index 
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Fejzić, Hajrudin; Mařík, Jan; Weil, Clifford E. Extending Peano derivatives. Mathematica Bohemica, Tome 119 (1994) no. 4, pp. 387-406. doi : 10.21136/MB.1994.126113. http://geodesic.mathdoc.fr/articles/10.21136/MB.1994.126113/

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