Efficient analytic continuation of power series by matrix summation methods (Q1409781)

The authors investigate some problems of efficient analytic continuation of power series in the plane \(\mathbb C\) by means of summability methods. They describe a new class of sets differing from domains allowing efficient summation (Theorem 1). In Section 3 they prove the existence of such matrix summation methods that are sufficient for the restoration of the analytic continuation of power series in a fixed point of a domain \(\Omega \subset \mathbb C\) without any additional conditions on \(\Omega.\)