Multiplicative Cauchy functional equation on symmetric cones

TL;DR

This paper solves the multiplicative Cauchy functional equation on symmetric cones using two different multiplication algorithms without requiring regularity assumptions on the functions.

Contribution

It provides a solution to the functional equation on symmetric cones under minimal assumptions, expanding understanding of functional equations in this mathematical context.

Findings

Solution to the functional equation on symmetric cones

Applicable to two different multiplication algorithms

No regularity assumptions needed

Abstract

We solve the multiplicative Cauchy functional equation on symmetric cones with respect to two different multiplication algorithms. We impose no regularity assumptions on respective functions.