Tauberian theorems between the logarithmic and Abel-type summability methods

David Borwein and Bruce Brigham Watson

Vol. 101 (1982), No. 1, 11–23

DOI: 10.2140/pjm.1982.101.11

Abstract

The object of this paper is to show that if a series is summable by the logarithmic method L, then the series is also summable by the Abel method A_λ, provided a tauberian condition of the “slowly decreasing” type is satisfied.

Mathematical Subject Classification 2000

Primary: 40G10

Secondary: 40E05

Milestones

Received: 30 July 1979

Revised: 2 June 1981

Published: 1 July 1982