Abstract
In this paper, we show that an inner functionf has finite entropy if and only if its derivativef′ lies in the Nevanlinna class. We prove also that the entropy off is given by the average of the logarithm of |f′|. The proof is based on the fact that, evenf being highly discontinuous on the circle, the action off −n on Borel subsets is smooth.
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Craizer, M. Entropy of inner functions. Israel J. Math. 74, 129–168 (1991). https://doi.org/10.1007/BF02775784
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DOI: https://doi.org/10.1007/BF02775784