A functional equation related to symmetry of operators |
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| Authors: | Michael Schwarzenberger |
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| Affiliation: | 1.Institut für Mathematische Stochastik,Dresden,Germany;2.Institute of Machine Tools and Control Engineering,Dresden,Germany |
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| 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 Lévy-driven Ornstein–Uhlenbeck process. |
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