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Fejzić, Hajrudin ; Mařík, Jan ; Weil, Clifford E.
Extending Peano derivatives. (English). Mathematica Bohemica, vol. 119 (1994), issue 4, pp. 387-406
MSC: 26A24 | MR 1316592 | Zbl 0824.26003 | DOI: 10.21136/MB.1994.126113
Keywords:
Peano derivatives; Denjoy index
Summary:
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 $i=1,2,\ldots,k$.
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