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A complex-variable proof of the Wiener tauberian theorem

Jean Esterlé (1980)

Annales de l'institut Fourier

The fundamental semigroup ( a t ) t > 0 of the heat equation for the real line has an analytic extension ( a t ) Re t > 0 to the right-hand open half plane which satisfies ∥ a t ∥ ≤ | t | for Re t ≥ 1 . Using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane we show that the Wiener tauberian theorem for L 1 ( R ) follows from the above inequality.

A quantified Tauberian theorem for sequences

David Seifert (2015)

Studia Mathematica

The main result of this paper is a quantified version of Ingham's Tauberian theorem for bounded vector-valued sequences rather than functions. It gives an estimate on the rate of decay of such a sequence in terms of the behaviour of a certain boundary function, with the quality of the estimate depending on the degree of smoothness this boundary function is assumed to possess. The result is then used to give a new proof of the quantified Katznelson-Tzafriri theorem recently obtained by the author...

A Tauberian theorem for distributions

Jiří Čížek, Jiří Jelínek (1996)

Commentationes Mathematicae Universitatis Carolinae

The well-known general Tauberian theorem of N. Wiener is formulated and proved for distributions in the place of functions and its Ganelius' formulation is corrected. Some changes of assumptions of this theorem are discussed, too.

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