Cauchy's functional equation and extensions: Goldie's equation and inequality, the Gołąb-Schinzel equation and Beurling's equation
arXiv:1405.3947
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.
Companion paper to: Additivity, subadditivity and linearity: automatic continuity and quantifier weakening