What is Wielandt theorem?

In mathematics, the Wielandt theorem characterizes the gamma function, defined for all complex numbers z {\displaystyle z} for which R e z > 0 {\displaystyle \mathrm {Re} \,z>0} by

as the only function f {\displaystyle f} defined on the half-plane H := { z ∈ C : Re z > 0 } {\displaystyle H:=\{z\in \mathbb {C} :\operatorname {Re} \,z>0\}} such that:

This theorem named after the mathematician Helmut Wielandt.