On regularity of linear summation methods of Taylor series. (English) Zbl 1340.40010

The authors find necessary and sufficient conditions for regularity of a summation method (defined by an infinite matrix) for the Taylor series of functions analytic on the unit disk \(D\) and continuous on \(\bar{D}\). The case of triangular matrices was studied by L. V. Taĭkov [Izv. Akad. Nauk SSSR, Ser. Mat. 26, 625–630 (1962; Zbl 0133.31002)].


40C05 Matrix methods for summability
30B10 Power series (including lacunary series) in one complex variable


Zbl 0133.31002