Shapovalovska L. Asymptotic properties of analytic functions in the polydisk

In the thesis Levy's phenomenon for analogue of Wiman's inequality in the class of entire functions of several complex variables with rapidly oscilating coefficients are investigated. Sharp analogues of Wiman's and Kovary's inequalities in the class of analytic functions in DxC are proved. Also sharp analogues of Kovary's inequalities in the class of analytic functions in the unit polydisc are obtained. The distribution of the abscissa of convergence of random Dirichlet series and distribution of radii of convergence lacunary power series with pairwise independent and in general non identically distributed random coefficients are investigated.