Tauberian theorems for matrices generated by analytic functions

John Albert Fridy and Robert Ellis Powell

Vol. 92 (1981), No. 1, 79–85

DOI: 10.2140/pjm.1981.92.79

Abstract

Several classes of summability matrices are determined by the coefficients of Maclaurin series of the products of certain analytic functions. These matrices include generalizations of the transforms of Lototsky, Taylor, and others. It is proved that under rather weak restrictions on the analytic functions, x_k − x_k+1 = o(k⁻¹) is a Tauberian condition for the resulting matrix transformations.

Mathematical Subject Classification 2000

Primary: 40G05

Secondary: 40C15, 40E05

Milestones

Received: 14 June 1979

Published: 1 January 1981