Extending Peano derivatives

Fejzić, Hajrudin, Mařík, Jan, and Weil, Clifford E.. "Extending Peano derivatives." Mathematica Bohemica 119.4 (1994): 387-406. <http://eudml.org/doc/29267>.

@article{Fejzić1994,
abstract = {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 $i=1,2,\ldots ,k$.},
author = {Fejzić, Hajrudin, Mařík, Jan, Weil, Clifford E.},
journal = {Mathematica Bohemica},
keywords = {Peano derivatives; Denjoy index; Peano derivatives; Denjoy index},
language = {eng},
number = {4},
pages = {387-406},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Extending Peano derivatives},
url = {http://eudml.org/doc/29267},
volume = {119},
year = {1994},
}

TY - JOUR
AU - Fejzić, Hajrudin
AU - Mařík, Jan
AU - Weil, Clifford E.
TI - Extending Peano derivatives
JO - Mathematica Bohemica
PY - 1994
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 119
IS - 4
SP - 387
EP - 406
AB - 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 $i=1,2,\ldots ,k$.
LA - eng
KW - Peano derivatives; Denjoy index; Peano derivatives; Denjoy index
UR - http://eudml.org/doc/29267
ER -