Argument of bounded analytic functions and Frostman's type conditions [article]

Igor Chyzhykov
2009 arXiv   pre-print
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 f(z), f∈ H^∞, and the local concentration of the zeros of f.
arXiv:0906.1138v1 fatcat:fpwcxns3bnh4ff6t542ti3e5ai