Argument of bounded analytic functions and Frostman's type conditions

Details Argument of bounded analytic functions and Frostman's type conditions Argument of bounded analytic functions and Frostman's type conditions

2009-06-05

arxiv.org/abs/0906.1138v1

Mathematics

Complex Variables

17 pages

Scientific paper

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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