Tauberian conclusions

A Tauberian Theorem for Stretchings

R. C. Buck fl] has shown that if a regular matrix sums every subsequence of a sequence x, then x is convergent. I. J. Maddox [4] improved Buck's theorem by showing that if a non-Schur matrix sums every subsequence of a sequence x, then x is convergent. Actually Maddox proved a stronger result: If x is divergent and A sums every subsequence of x, then A is a Schur matrix, i.e., It should be rema...

On Tauber’s Second Tauberian Theorem

We study Tauberian conditions for the existence of Cesàro limits in terms of the Laplace transform. We also analyze Tauberian theorems for the existence of distributional point values in terms of analytic representations. The development of these theorems is parallel to Tauber’s second theorem on the converse of Abel’s theorem. For Schwartz distributions, we obtain extensions of many classical ...

The Wiener-Pitt tauberian theorem

Tauberian theorems for sum sets

Introduction. The sums formed from the set of non-negative powers of 2 are just the non-negative integers. It is easy to obtain “abelian” results to the effect that if a set is distributed like the powers of 2, then the sum set will be distributed like Dhe non-negative integers. We will be concerned here with converse, or “Tauberian” results. The main theme of this paper is t’he following quest...

Set Quantities and Tauberian Operators

The concept of convexity plays an important role in the classical geometry of normed spaces and it is frequently used in several branches of nonlinear analysis. In recent years some papers that contain generalizations of the concept of convexity with the help of the measures of noncompactness have appeared. The Tauberian operators were introduced by Kalton and Wilansky (1976) and they appear in...