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

top
Let K be a perfect compact set, E a quasi-complete locally convex space over 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

top

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

top
  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

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.