Extension and division on complex manifolds (Q2749823)

The author is busy with extension and division in the theory of holomorphic \(L^2\)-functions. In the first section he gives a survey of the theory of \(L^2\) extension on complex manifolds. In the second section he sketches Skoda's \(L^2\) division theory published in 1972, 1978. In the third section the author shows how the \(L^2\) extension theory implies an \(L^2\) division theorem. As corollary he gets a theorem on representation of a holomorphic function \(f\) on a bounded pseudoconvex domain \(D\) in \(\mathbb{C}^n\) in the form \(f(z)= \sum^n_{j=1} z_jg_j(z)\), \(g_j\in {\mathcal O}(D)\).NEWLINENEWLINEFor the entire collection see [Zbl 0963.00016].