Abstract:
The Koenigs function arises as the limit of an appropriately normalized sequence of iterates of holomorphic functions. On the other hand it is a solution of a certain functional equation and can be used for the definition of iterates of the original function.
A description of the class of Koenigs functions corresponding to probability generating functions embeddable in a one-parameter group of fractional iterates is provided. The results obtained can be regarded as a test for the embeddability of a Galton–Watson process
in a homogeneous Markov branching process.
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