Statistical extensions of some classical Tauberian theorems in nondiscrete setting

• Autorzy: Ferenc Móricz
• Języki publikacji: EN

Abstrakty

EN

Schmidt's classical Tauberian theorem says that if a sequence $(s_{k}: k = 0,1,...)$ of real numbers is summable (C,1) to a finite limit and slowly decreasing, then it converges to the same limit. In this paper, we prove a nondiscrete version of Schmidt's theorem in the setting of statistical summability (C,1) of real-valued functions that are slowly decreasing on ℝ ₊. We prove another Tauberian theorem in the case of complex-valued functions that are slowly oscillating on ℝ ₊. In the proofs we make use of two nondiscrete analogues of the famous Vijayaraghavan lemma, which seem to be new and may be useful in other contexts.

Kategorie tematyczne

• 40E05: Tauberian theorems, general
• 40C10: Integral methods
• 40G05: Ces\`aro, Euler, N\"orlund and Hausdorff methods

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 107
• Numer: 1
• Strony: 45-56

Daty

wydano

2007

Twórcy

autor

Ferenc Móricz

• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary

Identyfikatory

DOI

10.4064/cm107-1-6