Manne, Per E. Carleman approximation on totally real subsets of class \(C^ k\). (English) Zbl 0843.32005 Math. Scand. 74, No. 2, 313-319 (1994). 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 \(C^k(S)\). Reviewer: P.Boyadjiev (Gabes) Cited in 1 Document MSC: 32Q99 Complex manifolds Keywords:Carleman approximation; totally real subset of class \(C^ k\) PDFBibTeX XMLCite \textit{P. E. Manne}, Math. Scand. 74, No. 2, 313--319 (1994; Zbl 0843.32005) Full Text: DOI EuDML