Bounded separation of singularities of analytic functions (Q2782546)

Let \(\Omega\) be an open set in the extended complex plane \(\overline{\mathbb{C}}\). Consider a pair \((k_1,k_2)\) of closed subsets of \(\Omega\) and put \(k=k_1\cup k_2\). A classical theorem asserts that for every \(f\) analytic in \(\Omega\setminus k\), there exist a pair of functions \(f_j\) analytic in \(\Omega\setminus k_j, j=1,2 \) such that \(f=f_1+f_2\) in \(\Omega\setminus k\); so we have separation of singularities. The authors study the analogous problem for bounded analytic functions. They use Cauchy potentials and the Vitushkin localization operator to obtain some partial results on that problem. They obtain stronger results in various special cases for the sets \(k_1,k_2\).NEWLINENEWLINEFor the entire collection see [Zbl 0980.00031].