Abel and Fabry properties of basis decompositions of analytic functions (Q1603077)

Let \(G\) be a simply connected domain in the extended plane \(\mathbb{C}\), \(A(G)\) be the space of analytic functions in \(G\) with the topology of interior uniform convergence, \(\overline A(\mathbb{C}\backslash G)\) be the dual space to \(A(G)\). Let \(D\) be an arbitrary simply connected domain, \(G\subset D\). The author has investigated the problem of the continuation of a common basis of the spaces \(A(G)\) and \(\overline A(\overline G)\) into \(D\) as the basis of \(A(D)\).