| Title:
|
A characterization of holomorphic germs on compact perfect sets (English) |
| Author:
|
Carboni, Graciela |
| Author:
|
Larotonda, Angel |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
483-490 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $K\subseteq\Bbb C$ be a perfect compact set, $E$ a quasi-complete locally convex space over $\Bbb C$ and $f:K\to E$ a map. In this note we give a necessary and sufficient condition --- in terms of differential quotients --- for $f$ to have a holomorphic extension on a neighborhood of $K$. (English) |
| Keyword:
|
differential quotients |
| Keyword:
|
holomorphic extensions |
| MSC:
|
30B40 |
| MSC:
|
46G20 |
| MSC:
|
46J15 |
| MSC:
|
46J40 |
| idZBL:
|
Zbl 1103.46022 |
| idMR:
|
MR2103142 |
| . |
| Date available:
|
2009-05-05T16:46:43Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119475 |
| . |
| Reference:
|
[1] Bochnak J., Siciak J.: Analytic functions in topological spaces.Studia Math. (1971), 39 77-112. MR 0313811 |
| Reference:
|
[2] Dales H.G., Davie A.: Quasianalytic Banach function algebras.J. Funct. Anal. (1973), 13 28-50. Zbl 0254.46027, MR 0343038 |
| Reference:
|
[3] Grothendieck A.: Sur certains espaces de fonctions holomorphes. I-II.J. Reine Angew. Math. (1953), 192 35-64, 77-95. Zbl 0051.08704, MR 0058865 |
| Reference:
|
[4] Kriegl A., Michor P.: The convenient setting of global analysis.Mathematical Surveys and Monograps, 53 (Chapter III), American Mathematical Society, Providence, RI, 1997. Zbl 0889.58001, MR 1471480 |
| Reference:
|
[5] Malgrange B.: Ideals of Differentiable Functions.Oxford Univ. Press, London, 1966. Zbl 0177.18001, MR 0212575 |
| Reference:
|
[6] Tougeron J.C.: Idéaux de fonctions différentiables.Ergebrisse 71, Springer, Heidelberg, 1972. Zbl 0251.58001, MR 0440598 |
| . |
