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Carleman approximation on totally real subsets of class $$C^ k$$. (English) Zbl 0843.32005
Let $$X$$ be a complex manifold and $$S \subset X$$ a totally real subset of class $$C^k$$, such that there is a non-negative function $$\rho \in C^{k + 1} (X)$$, which is strictly plurisubharmonic on a neighborhood of $$S$$ and such that $$S = \rho^{-1} (0)$$. It is shown that there exists a Stein neighborhood $$\Omega$$ of $$S$$ in $$X$$ such that $$O(\Omega)$$ is dense in $$C^k(S)$$ in the so called Whitney $$C^k$$-topology on $$C^k(S)$$.

##### MSC:
 32Q99 Complex manifolds
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