The Corona problem in Carleman algebras on Stein manifolds (Q860139)

If \(\Omega\) is a relatively compact Stein open subset of a complex manifold \(X\), the author provides a condition under which a finite set of holomorphic functions in the Carleman algebra \(A_{p} (\Omega)\) (the algebra of holomorphic functions in \(\Omega\) for which there exist some positive constants \(c_{1}\) and \(c_{2}\) such that \( | f(z)| \leq c_{1} \exp(c_{2}p(z))\) for each \(z \in \Omega\)) generates this algebra. Further \(L^{2}\) estimates for the \(\overline {\partial}\)-operator on Stein manifolds are also presented.