A remark on the approximation theorems of Whitney and Carleman-Scheinberg
Commentationes Mathematicae Universitatis Carolinae (2015)
- Volume: 56, Issue: 1, page 1-6
- ISSN: 0010-2628
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topJohanis, Michal. "A remark on the approximation theorems of Whitney and Carleman-Scheinberg." Commentationes Mathematicae Universitatis Carolinae 56.1 (2015): 1-6. <http://eudml.org/doc/269884>.
@article{Johanis2015,
abstract = {We show that a $C^k$-smooth mapping on an open subset of $\mathbb \{R\}^n$, $k\in \mathbb \{N\}\cup \lbrace 0,\infty \rbrace $, can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.},
author = {Johanis, Michal},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {approximation; real-analytic; entire functions; approximation; real-analytic; entire functions},
language = {eng},
number = {1},
pages = {1-6},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A remark on the approximation theorems of Whitney and Carleman-Scheinberg},
url = {http://eudml.org/doc/269884},
volume = {56},
year = {2015},
}
TY - JOUR
AU - Johanis, Michal
TI - A remark on the approximation theorems of Whitney and Carleman-Scheinberg
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 1
SP - 1
EP - 6
AB - We show that a $C^k$-smooth mapping on an open subset of $\mathbb {R}^n$, $k\in \mathbb {N}\cup \lbrace 0,\infty \rbrace $, can be approximated in a fine topology and together with its derivatives by a restriction of a holomorphic mapping with explicitly described domain. As a corollary we obtain a generalisation of the Carleman-Scheinberg theorem on approximation by entire functions.
LA - eng
KW - approximation; real-analytic; entire functions; approximation; real-analytic; entire functions
UR - http://eudml.org/doc/269884
ER -
References
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