Illinois Journal of Mathematics

Argument of bounded analytic functions and Frostman’s type conditions

Igor Chyzhykov

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We describe the growth of the naturally defined argument of a bounded analytic function in the unit disk in terms of the complete measure introduced by A. Grishin. As a consequence, we characterize the local behavior of a logarithm of an analytic function. We also find necessary and sufficient conditions for closeness of $\log f(z)$, $f\in H^\infty$, and the local concentration of the zeros of $f$.

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Illinois J. Math., Volume 53, Number 2 (2009), 515-531.

First available in Project Euclid: 23 February 2010

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Primary: 30D50


Chyzhykov, Igor. Argument of bounded analytic functions and Frostman’s type conditions. Illinois J. Math. 53 (2009), no. 2, 515--531. doi:10.1215/ijm/1266934790.

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