SUMMABILITY OF POWER-SERIES BY NONREGULAR NORLUND-METHODS

Given a regular Nörlund-method (N, p) one can prove that the sequence {σn(z)} of the Nörlund-transforms of a power series f{hook}(z) = ∑v = 0∞ avzv with radius of convergence r = 1 converges in at most countably many points outside the unit disc. In this paper we show that for a class of non-regular Nörlund-methods the sequence {σn(z)} converges to an analytic function in a disc which strictly contains the unit disc, and the convergence is uniform on any compact subset of this disc. © 1992.