Argument of bounded analytic functions and Frostman's type conditions

Igor Chyzhykov

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arXiv · 0906.1138

Argument of bounded analytic functions and Frostman's type conditions

Igor Chyzhykov

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Abstract

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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Igor Chyzhykov. 2009-06-05. Argument of bounded analytic functions and Frostman's type conditions. https://arxiv.org/abs/0906.1138

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