## Illinois Journal of Mathematics

### Argument of bounded analytic functions and Frostman’s type conditions

Igor Chyzhykov

#### 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 $f$.

#### Article information

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

Dates
First available in Project Euclid: 23 February 2010

https://projecteuclid.org/euclid.ijm/1266934790

Digital Object Identifier
doi:10.1215/ijm/1266934790

Mathematical Reviews number (MathSciNet)
MR2594641

Zentralblatt MATH identifier
1188.30063

Subjects
Primary: 30D50

#### Citation

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. https://projecteuclid.org/euclid.ijm/1266934790

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