Tauberian theorems via block dominated matrices

John Albert Fridy

Vol. 81 (1979), No. 1, 81–91

DOI: 10.2140/pjm.1979.81.81

Abstract

The principle result is a general Tauberian theorem that can be applied to any regular real matrix summability method. The Tauberian condition is determined by the lengths of the blocks of consecutive terms that dominate the rows of the matrix. This theorem and its variants are then used to give a unified method of proving some of the classical Tauberian theorems for the methods of Abel, Borel, and Euler-Knopp. The general technique is also used to prove new Tauberian theorems for Nörlund and Taylor matrices.

Mathematical Subject Classification 2000

Primary: 40E05

Milestones

Received: 12 June 1978

Published: 1 March 1979