# 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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- Nersesyan A., On Carleman sets, Amer. Math. Soc. Transl. Ser. 2 122 (1984), 99–104. Zbl0552.30029
- Scheinberg S., 10.1007/BF02789974, J. Analyse Math. 29 (1976), 16–18. Zbl0343.41022MR0508100DOI10.1007/BF02789974
- Whitney H., 10.1090/S0002-9947-1934-1501735-3, Trans. Amer. Math. Soc. 36 (1934), no. 1, 63–89. Zbl0008.24902MR1501735DOI10.1090/S0002-9947-1934-1501735-3

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