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I have been working through the proof of Cartan's Theorem B that Hörmander gives in his book 'Introduction to Complex Analysis in Several Variables'. When I began, I skipped over some of the initial ...

Let $M$ be a Stein manifold with smooth, strictly pseudoconvex boundary, and $x$ a point on its boundary. Is there a holomorphic function $f$ on $M$, smooth on the boundary, with strict maximum of $|f|...

Let $Y \to M$ be a (proper and locally trivial) family of relatively compact strictly pseudoconvex domains which are smooth (not neccesarily Stein spaces). So $Y$ and $M$ are a complex manifold and ...

Let $X$ be a Stein manifold, $K$ be a compact subset of $X$. Consider the following conditions: 1.$K$ admit an open neighborhood basis in $X$ whose members are Stein; 2.$K=\cap_{j\ge 1}V_j$, where $...

Let $D$ be a either an open polydisc or an open ball in $\mathbf{C}^n$. (1) Let $\mathcal{O}$ be the $\mathbf{C}$-algebra of holomorphic functions on $\mathbf{C}^n$, resp. $D$, and let $f_1,\ldots, ...