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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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