A trivial Tauberian theorem

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...

A uniform Tauberian theorem in optimal control

In an optimal control framework, we consider the value VT (x) of the problem starting from state x with finite horizon T , as well as the value Wλ(x) of the λ-discounted problem starting from x. We prove that uniform convergence (on the set of states) of the values VT (·) as T tends to infinity is equivalent to uniform convergence of the values Wλ(·) as λ tends to 0, and that the limits are ide...

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 ...

A Tauberian theorem for Ingham summation method

The aim of this work is to prove a Tauberian theorem for the Ingham summability method. The Taube-rian theorem we prove can be used to analyze asymptotics of mean values of multiplicative functions on natural numbers.

The Wiener-Pitt tauberian theorem