 Denjoy–Carleman–Ahlfors theorem

The Denjoy–Carleman–Ahlfors theorem is a result in complex analysis concerning analytic functions and their growth properties. It deals specifically with the behavior of holomorphic functions in relation to their logarithmic growth. The theorem states that if \( f(z) \) is a holomorphic function on a domain in the complex plane and \( f(z) \) satisfies a certain growth condition, then the order of the entire function can be characterized more concretely.