no. 2
An approximation theorem related to good compact sets in the sense of Martineau
Annales de l'Institut Fourier, Tome 50 (2000) no. 2, pp. 677-687.
corrigé par Corrigendum - An approximation theorem related to good compact sets in the sense of Martineau
[Un théorème d'approximation lié à la notion de bon compact au sens de Martineau]

On établit un théorème d’approximation qui implique que tout sous-ensemble compact de ℂ n est un bon compact au sens de Martineau. Il s’agit d’une propriété d’approximation cruciale pour l’extension des fonctionnelles analytiques. Le théorème d’approximation est fondé sur un résultat de finitude pour les enveloppes polynomiales.

This note contains an approximation theorem that implies that every compact subset of ℂ n is a good compact set in the sense of Martineau. The property in question is fundamental for the extension of analytic functionals. The approximation theorem depends on a finiteness result about certain polynomially convex hulls.

@article{AIF_2000__50_2_677_0,
     author = {Rosay, Jean-Pierre and Stout, Edgar Lee},
     title = {An approximation theorem related to good compact sets in the sense of {Martineau}},
     journal = {Annales de l'Institut Fourier},
     pages = {677--687},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
     number = {2},
     year = {2000},
     doi = {10.5802/aif.1768},
     zbl = {0964.32010},
     mrnumber = {2001g:32026},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1768/}
}
TY  - JOUR
AU  - Rosay, Jean-Pierre
AU  - Stout, Edgar Lee
TI  - An approximation theorem related to good compact sets in the sense of Martineau
JO  - Annales de l'Institut Fourier
PY  - 2000
SP  - 677
EP  - 687
VL  - 50
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - https://aif.centre-mersenne.org/articles/10.5802/aif.1768/
DO  - 10.5802/aif.1768
LA  - en
ID  - AIF_2000__50_2_677_0
ER  - 
%0 Journal Article
%A Rosay, Jean-Pierre
%A Stout, Edgar Lee
%T An approximation theorem related to good compact sets in the sense of Martineau
%J Annales de l'Institut Fourier
%D 2000
%P 677-687
%V 50
%N 2
%I Association des Annales de l’institut Fourier
%U https://aif.centre-mersenne.org/articles/10.5802/aif.1768/
%R 10.5802/aif.1768
%G en
%F AIF_2000__50_2_677_0
Rosay, Jean-Pierre; Stout, Edgar Lee. An approximation theorem related to good compact sets in the sense of Martineau. Annales de l'Institut Fourier, Tome 50 (2000) no. 2, pp. 677-687. doi : 10.5802/aif.1768. https://aif.centre-mersenne.org/articles/10.5802/aif.1768/

[1] E. Bishop, Holomorphic completions, analytic continuations, and the interpolation of semi-norms, Ann. Math., 78 (1963), 468-500. | Zbl

[2] J.E. Björk, Every compact set in ℂn is a good compact set, Ann. Inst. Fourier, Grenoble, 20-1 (1970), 493-498. | Numdam | Zbl

[3] R.C. Gunning, Introduction to Holomorphic Functions of Several Complex Variables, vol. I, Wadsworth and Brooks-Cole, Belmont, 1990.

[4] R.C. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall, Englewood Cliffs, 1965. | MR | Zbl

[5] A. Martineau, Sur les fonctionnelles analytiques et la transformation de Fourier-Borel, J. Analyse Math., XI (1963), 1-164. (Also contained in the Œuvres of Martineau). | MR | Zbl

[6] J.-P. Rosay and E.L. Stout, Strong boundary values, analytic functionals and nonlinear Paley-Wiener theory, to appear.

[7] W.R. Zame, Algebras of analytic germs, Trans. Amer. Math. Soc., 174 (1972), 275-288. | MR | Zbl

Cité par Sources :