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For infinite discrete additive semigroups $X \subset [0, \infty)$ we study normed algebras of arithmetic functions $g : X \to ℂ$ endowed with the linear operations and the convolution. In particular, we investigate the problem of scaling the mean deviation of related multiplicative functions for $X = log ℕ$ . This involves an extension of Banach algebras of arithmetic functions by introducing weight functions and proving a weighted inversion theorem of Wiener type in the frame of Gelfand’s theory of commutative Banach algebras.

Contributions to local and microlocal analysis, an overwiew

S. Pilipović (2010)

Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques

Correction to "A Generalization of Tauber's Theorem and Some Tauberian Constants (IV)".

C.T. Rajagopal (1976)

Mathematische Zeitschrift

Das Wachstumsverhalten ganzer Funktionen unter Voraussetzungen über ihre Laplace-Transformierte.

Jürgen Mäulen (1981)

Mathematische Zeitschrift

Distributional versions of Littlewood's Tauberian theorem

Ricardo Estrada, Jasson Vindas (2013)

Czechoslovak Mathematical Journal

We provide several general versions of Littlewood's Tauberian theorem. These versions are applicable to Laplace transforms of Schwartz distributions. We employ two types of Tauberian hypotheses; the first kind involves distributional boundedness, while the second type imposes a one-sided assumption on the Cesàro behavior of the distribution. We apply these Tauberian results to deduce a number of Tauberian theorems for power series and Stieltjes integrals where Cesàro summability follows from Abel...

Ein Tauber-Satz mit Restglied für die Laplace-Transformation.

Albert Stadler (1989)

Commentarii mathematici Helvetici

Elementary Tauberian Theorems For Regular Linear Operators

M. Vuileumier (1975)

Publications de l'Institut Mathématique

Elementary Tauberian theorems for regular linear operators.

M. Vuilleumier (1974)

Publications de l'Institut Mathématique [Elektronische Ressource]

Esterlè's proof of the tauberian theorem for Beurling algebras

H. G. Dales, W. K. Hayman (1981)

Annales de l'institut Fourier

Recently in this Journal J. Esterlé gave a new proof of the Wiener Tauberian theorem for $L^{1} (R)$ using the Ahlfors-Heins theorem for bounded analytic functions on a half-plane. We here use essentially the same method to prove the analogous result for Beurling algebras $L_{φ}^{1} (R)$ . Our estimates need a theorem of Hayman and Korenblum.

General Nörlund transforms and power series methods.

Rüdiger Kiesel (1993)

Mathematische Zeitschrift

General Tauberian Remainder Theorems.

Sonja Lyttkens (1974)

Mathematica Scandinavica

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