Geodesic
Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn
Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 522-526

Voir la notice de l'article provenant de la source Cambridge University Press

Let L 1, L 2 ⊂ Cn be two totally real subspaces of real dimension n, and such that L 1 ∩ L 2 = {0}. We show that continuous functions on L 1 ∪L 2 allow Carleman approximation by entire functions if and only if L 1 ∪L 2 is polynomially convex. If the latter condition is satisfied, then a function f:L 1 ∪L 2 —> C such that f|L iCk(Li), i = 1,2, allows Carleman approximation of order k by entire functions if and only if f satisfies the Cauchy-Riemann equations up to order k at the origin.
DOI : 10.4153/CMB-1994-075-3
Mots-clés : 32E30 
Manne, Per E. Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn. Canadian mathematical bulletin, Tome 37 (1994) no. 4, pp. 522-526. doi: 10.4153/CMB-1994-075-3
@article{10_4153_CMB_1994_075_3,
     author = {Manne, Per E.},
     title = {Carleman {Approximation} by {Entire} {Functions} on the {Union} of {Two} {Totally} {Real} {Subspaces} of {Cn}},
     journal = {Canadian mathematical bulletin},
     pages = {522--526},
     year = {1994},
     volume = {37},
     number = {4},
     doi = {10.4153/CMB-1994-075-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-075-3/}
}
TY  - JOUR
AU  - Manne, Per E.
TI  - Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn
JO  - Canadian mathematical bulletin
PY  - 1994
SP  - 522
EP  - 526
VL  - 37
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-075-3/
DO  - 10.4153/CMB-1994-075-3
ID  - 10_4153_CMB_1994_075_3
ER  - 
%0 Journal Article
%A Manne, Per E.
%T Carleman Approximation by Entire Functions on the Union of Two Totally Real Subspaces of Cn
%J Canadian mathematical bulletin
%D 1994
%P 522-526
%V 37
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1994-075-3/
%R 10.4153/CMB-1994-075-3
%F 10_4153_CMB_1994_075_3

[1] 1. Frih, E. M., Approximation holomorphe globale sur Vunion de deux sous-espaces totalement réels maximaux de Cn, Canad. Math. Bull. 34(1991), 215–219. Google Scholar

[2] 2. Manne, P., Carle man Approximation on Totally Real Submanifolds of a Complex Manifold, In: Several Complex Variables: Proceedings of the Mittag-Leffler Institute, 1987-1988, (ed. J. E. Fornaess), Princeton University Press, New Jersey, 1993. Google Scholar

[3] 3. Range, R. M. and Siu, Y.-T., Ck Approximation by Holomorphic Functions and -Closed Forms on Ck Submanifolds of a Complex Manifold, Math. Ann. 210(1974), 105–122. Google Scholar

[4] 4. Stout, E. L. and Zame, W. R., Totally Real Imbeddings and the Universal Covering Spaces of Domains of Holomorphy: Some Examples, Manuscripta Math. 50(1985), 29–48. Google Scholar

[5] 5. Weinstock, B., On the Polynomial Convexity of the Union of Two Maximal Totally Real Subspaces of Cn, Math. Ann. 282(1988), 131–138. Google Scholar

Cité par Sources :