On the limit-3 classification of the square of a second-order, linear differential expression

William Norrie Everitt; Magnus Giertz

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Extending Peano derivatives

Hajrudin Fejzić, Jan Mařík, Clifford E. Weil (1994)

Mathematica Bohemica

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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 $i = 1, 2, ..., k$ .