On ( h(n)) summability methods

TL;DR: The h(n) summability methods are established for being conservative and absolutely conservative.

Abstract: Abstract In 1967 Segal introduced the Dirichlet convolution (, h(n)), generalizing a method of Ingham developed in studies on the Prime Number Theorem. In this paper we establish necessary and sufficient conditions on the sequence h(n) in order that the convolution method (, h(n)) be conservative. Further conditions are established for the method to be absolutely conservative.