| Title:
|
A remark on the approximation theorems of Whitney and Carleman-Scheinberg (English) |
| Author:
|
Johanis, Michal |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
56 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
|
1-6 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We show that a $C^k$-smooth mapping on an open subset of $\mathbb R^n$, $k\in \mathbb N\cup\{0,\infty\}$, 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. (English) |
| Keyword:
|
approximation |
| Keyword:
|
real-analytic |
| Keyword:
|
entire functions |
| MSC:
|
41A30 |
| MSC:
|
46T20 |
| MSC:
|
46T25 |
| idZBL:
|
Zbl 06433801 |
| idMR:
|
MR3311573 |
| DOI:
|
10.14712/1213-7243.015.101 |
| . |
| Date available:
|
2015-03-10T17:29:13Z |
| Last updated:
|
2017-04-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144182 |
| . |
| Reference:
|
[C] Carleman T.: Sur un théorème de Weierstrass.(French), Ark. Mat., Ast. Fysik 20B (1927), no. 4, 1–5. |
| Reference:
|
[FG] Frih E.M., Gauthier P.M.: Approximation of a function and its derivatives by entire functions of several variables.Canad. Math. Bull. 31 (1988), no. 4, 495–499. Zbl 0641.32011, MR 0971578, 10.4153/CMB-1988-071-1 |
| Reference:
|
[FHHMZ] Fabian M., Habala P., Hájek P., Montesinos V., Zizler V.: Banach Space Theory.CMS Books in Mathematics, Springer, New York, 2011. Zbl 1229.46001, MR 2766381 |
| Reference:
|
[Hi] Hille E.: Functional analysis and semi-groups.Amer. Math. Soc. Colloq. Publ. 31, American Mathematical Society, New York, 1948. Zbl 0392.46001, MR 0025077 |
| Reference:
|
[Ho] Hoischen L.: Eine Verschärfung eines Approximationssatzes von Carleman.(German), J. Approx. Theory 9 (1973), no. 3, 272–277. Zbl 0271.30035, MR 0367217, 10.1016/0021-9045(73)90093-2 |
| Reference:
|
[K] Kaplan W.: Approximation by entire functions.Michigan Math. J. 3 (1955), no. 1, 43–52. Zbl 0070.06203, MR 0070753, 10.1307/mmj/1031710533 |
| Reference:
|
[N] Nersesyan A.: On Carleman sets.Amer. Math. Soc. Transl. Ser. 2 122 (1984), 99–104. Zbl 0552.30029 |
| Reference:
|
[S] Scheinberg S.: Uniform approximation by entire functions.J. Analyse Math. 29 (1976), 16–18. Zbl 0343.41022, MR 0508100, 10.1007/BF02789974 |
| Reference:
|
[W] Whitney H.: Analytic extensions of differentiable functions defined in closed sets.Trans. Amer. Math. Soc. 36 (1934), no. 1, 63–89. Zbl 0008.24902, MR 1501735, 10.1090/S0002-9947-1934-1501735-3 |
| . |
