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
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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.
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/}
}
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