A characterization of holomorphic germs on compact perfect sets

Graciela Carboni; Angel Rafael Larotonda

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 3, page 483-490
  • ISSN: 0010-2628

Abstract

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Let K ⊆ ℂ be a perfect compact set, E a quasi-complete locally convex space over ℂ and f : K → 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 .

How to cite

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Carboni, Graciela, and Larotonda, Angel Rafael. "A characterization of holomorphic germs on compact perfect sets." Commentationes Mathematicae Universitatis Carolinae 45.3 (2004): 483-490. <http://eudml.org/doc/249368>.

@article{Carboni2004,
abstract = {Let $K\subseteq \mathbb \{C\}$ be a perfect compact set, $E$ a quasi-complete locally convex space over $\mathbb \{C\}$ and $f:K\rightarrow E$ 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 $K$.},
author = {Carboni, Graciela, Larotonda, Angel Rafael},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {differential quotients; holomorphic extensions; difference quotients; holomorphic extensions},
language = {eng},
number = {3},
pages = {483-490},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A characterization of holomorphic germs on compact perfect sets},
url = {http://eudml.org/doc/249368},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Carboni, Graciela
AU - Larotonda, Angel Rafael
TI - A characterization of holomorphic germs on compact perfect sets
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 3
SP - 483
EP - 490
AB - Let $K\subseteq \mathbb {C}$ be a perfect compact set, $E$ a quasi-complete locally convex space over $\mathbb {C}$ and $f:K\rightarrow E$ 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 $K$.
LA - eng
KW - differential quotients; holomorphic extensions; difference quotients; holomorphic extensions
UR - http://eudml.org/doc/249368
ER -

References

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  1. Bochnak J., Siciak J., Analytic functions in topological spaces, Studia Math. (1971), 39 77-112. (1971) MR0313811
  2. Dales H.G., Davie A., Quasianalytic Banach function algebras, J. Funct. Anal. (1973), 13 28-50. (1973) Zbl0254.46027MR0343038
  3. Grothendieck A., Sur certains espaces de fonctions holomorphes. I-II, J. Reine Angew. Math. (1953), 192 35-64, 77-95. (1953) Zbl0051.08704MR0058865
  4. Kriegl A., Michor P., The convenient setting of global analysis, Mathematical Surveys and Monograps, 53 (Chapter III), American Mathematical Society, Providence, RI, 1997. Zbl0889.58001MR1471480
  5. Malgrange B., Ideals of Differentiable Functions, Oxford Univ. Press, London, 1966. Zbl0177.18001MR0212575
  6. Tougeron J.C., Idéaux de fonctions différentiables, Ergebrisse 71, Springer, Heidelberg, 1972. Zbl0251.58001MR0440598

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