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Approximation Holomorphe Globale Sur L'union de Deux Sous-Espaces Totalement Réels Maximaux de Cn

Published online by Cambridge University Press:  20 November 2018

El Mostapha Frih*
Affiliation:
Departement de Mathématiques et de Statistique Université de Montréal, Montréal (RQ) H3C 3J7, Canada
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Abstract

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Let E and F be real subspaces of Cn which contain no non trivial complex subspace of Cn and intersecting only at the origin. We prove in a special case that every continuous function on E ∪ F can be asymptotically approximated on E ∪ F by an entire function.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Gamelin, T. W., Uniform algebras, Prentice-Hall Inc., 1969.Google Scholar
2. Mergelyan, S. N., On the representation of functions by series of polynomials on closed sets (Russe), Dokl. Akad. Nauk SSSR NS 78 (1951), 405408. Amer. Math. Soc. Transi. 85 Providence 1953.Google Scholar
3. Rossi, H., Holomorphically convex sets in several complex variables, Ann. of Math. 74 (1961), 470493.Google Scholar
4. Scheinberg, S., Uniform approximation by entire functions, J. Anal. Mathématiques 24 (1976), 1618.Google Scholar
5. Sibony, N., Hakim, M., Boundary properties of holomorphic functions in the ball in Cn. Math. Ann. 276 (1988), 549555.Google Scholar
6. Weinstock, B. M., On the polynomial convexity of the union of two maximal totally maximal real subspaces ofC” Math. Ann. 282 (1988) 131138.Google Scholar