Tauberian Conditions of Slowly Decreasing Type for the Logarithmic Power Series Method

Abstract

Let be a sequence of real numbers. We say that osnTHORN is summable to n by the logarithmic power series method if It is well known that if the limit exists, then the limit also exists. In this paper, we determine Tauberian conditions of slowly decreasing type to obtain ordinary convergence of osnTHORN from its summability by logarithmic power series method. As a consequence of our result, we give a short proof of an earlier Tauberian theorem due to Kwee (Can J Math 20:1324-1331, 1968).