General regular variation, Popa groups and quantifier weakening

We introduce general regular variation, a theory of regular variation containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. The unifying theme is the Popa groups of our title viewed as locally compact abelian ordered topological groups, together with thei...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-03, Vol.483 (2), p.123610, Article 123610
Main Authors: Bingham, N.H., Ostaszewski, A.J.
Format: Article
Language:English
Subjects:
Beurling-Goldie functional equation
Beurling-Goldie inequality
Functional inequalities
General regular variation
Gołąb-Schinzel equation
Haar measure
Popa groups
Quantifier weakening
Regular variation
Subadditivity
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Summary:We introduce general regular variation, a theory of regular variation containing the existing Karamata, Bojanic-Karamata/de Haan and Beurling theories as special cases. The unifying theme is the Popa groups of our title viewed as locally compact abelian ordered topological groups, together with their Haar measure and Fourier theory. The power of this unified approach is shown by the simplification it brings to the whole area of quantifier weakening, so important in this field.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2019.123610