1. A functional equation related to symmetry of operators
- Author
-
Michael Schwarzenberger
- Subjects
Generator (category theory) ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,010103 numerical & computational mathematics ,Function (mathematics) ,Type (model theory) ,01 natural sciences ,Combinatorics ,Functional equation ,Discrete Mathematics and Combinatorics ,Interval (graph theory) ,0101 mathematics ,Symmetry (geometry) ,Mathematics - Abstract
In this note we determine the unique solution to the functional equation \(f(x + y) ( x- y) = \left( f(x) -f (y) \right) (x + y)\). We require no additional assumptions on the function \(f\). Moreover we solve this functional equation if \(f\) is only defined on a finite interval. The interest in this type of functional equation is motivated by the study of symmetrizing measures for (the generator of) a Levy-driven Ornstein–Uhlenbeck process.
- Published
- 2017