A Wiener Tauberian theorem for operators and functions

The Wiener-Pitt tauberian theorem

Wiener Tauberian Theorems for Vector - Valued Functions

Different versions of Wiener’s Tauberian theorem are discussed for the generalized group algebra LI(G,A) (of integrable functions on a locally compact abelian group G taking values in a commutative semisimple regular Banach algebra A) using A-valued Fourier transforms. A weak form of Wiener’s Tauberian property is introduced and it is proved that LI(G,A) is weakly Tauberian if and only if A is....

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...

Wiener Tauberian Theorems for Sl 2 ( R )

In this article we prove a Wiener Tauberian theorem for L(SL2(R)), 1 ≤ p < 2. Let G be the group SL2(R) and K its maximal compact subgroup SO(2,R). Let M be {±I}. We show that if the Fourier transforms of a set of functions in L(G) do not vanish simultaneously on any irreducible Lp− -tempered representation for some > 0, where they are assumed to be defined, and if for each M-type at least one ...

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.