Cauchy's functional equation and extensions: Goldie's equation and inequality, the Gołąb-Schinzel equation and Beurling's equation

2014/05/15 by N. H. Bingham, Bingham, N. H., A. J. Ostaszewski +1 · 1 citation
Mathematics · #26A03 #33B99 #34D05 #39A20 #39B22 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.CA #msc:26A03 #msc:33B99 #msc:34D05 #msc:39A20 #msc:39B22

paper · pdf · doi:10.48550/arxiv.1405.3947

Companion paper to: Additivity, subadditivity and linearity: automatic continuity and quantifier weakening

arxiv created 2014/06/02 · arxiv updated 2014/06/03

Abstract

The Cauchy functional equation is not only the most important single functional equation, it is also central to regular variation. Classical Karamata regular variation involves a functional equation and inequality due to Goldie; we study this, and its counterpart in Beurling regular variation, together with the related Gołąb-Schinzel equation.

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• Homomorphisms from Functional Equations: The Goldie Equation

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