A generalization in integral form of certain Tauberian theorems

[摘要] The purpose of this paper is to generalize in integral form certain Tauberian theorems, Tauber, Hardy, Littlewood, and landau were among the first to investigate the problem of finding sufficient conditions for the convergence of series known to be summable with respect to a given method of sustainability. Certain of their theorems, generalized in integral form, will be considered in this paper. The convergence of the partial sums Sn of the series considered may be thought of as the convergence to a limit of a stop function S(x)j where S(x) = Sn for n-1 < x

[发布机构] Rice University