A revisited Tauberian theorem for which slow decrease with respect to a weight function is a tauberian condition for the weighted mean summability of integrals over R

In this extended abstract, we present an alternative proof of a Tauberian theorem of slowly decreasing type with respect to the weight function due to Karamata [5] for the weighted mean summable real-valued integrals over R+ := [0, ∞). Some particular choices of weight functions provide alternative...

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Bibliographic Details
Main Author: Canak, Ibrahim
Format: Conference Proceeding
Language:English
Subjects:
Integrals
Theorems
Weighting functions
Online Access:Get full text
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Summary:In this extended abstract, we present an alternative proof of a Tauberian theorem of slowly decreasing type with respect to the weight function due to Karamata [5] for the weighted mean summable real-valued integrals over R+ := [0, ∞). Some particular choices of weight functions provide alternative proofs of some well-known Tauberian theorems given for several important summability methods.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0042366