Summability methods based on the Riemann zeta function (Q1094605)

This paper is a study of summability methods that are based on the Riemann zeta function. A limitation theorem is proved which gives a necessary condition for a sequence x to be zeta summable. A zeta summability matrix \(Z_ t\) associated with a real sequence t is introduced; a necessary and sufficient condition on the sequence t such that \(Z_ t\) maps \(\ell_ 1\) to \(\ell_ 1\) is established. Results comparing the strength of the zeta method to that of well-known summability methods are also investigated.