A tauberian theorem related to the modified Hankel transform

A generalization of Littlewood's Tauberian theorem for the Laplace transform

In this paper we will consider a Tauberian problem of the following kind: Suppose that and are two functions of bounded variation on any nite interval 0; T]; T > 0, and suppose that (0) = (0) = 0. If furthermore Z 1 0 e ?st dd(t) Z 1 0 e ?st dd(t); s ! 0+; (0.1) where satisses some kind of regularity condition and satisses a Tauberian condition, then (t) (t); t ! 1: (0.2) Here (0.2) means that ...

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...

The Wiener-Pitt tauberian theorem

The Hankel transform

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...