Tauberian theorems for matrices generated by analytic functions
John A. Fridy, Robert E. Powell · Pacific Journal of Mathematics · 1981
Several classes of summability matrices are determined by the coefficients of Maclaurin series of the products of certain analytic functions.These matrices include generalizations of the transforms of Lototsky, Taylor, and others.It is proved that under rather weak restrictions on the analytic functions, x k -x k +i = o(k~1) is a Tauberian condition for the resulting matrix transformations.