Hlova T. Generalized scales of the growth of analytic functions.

The growth of analytic functions defined by power series or Dirichlet series in the terms of generalized scales is investigated in the thesis. A necessary and sufficient condition on a sequence of indexes of Dirichlet series absolutely convergent in a half-plane and a function of comparison under which -type of this series is equal to -type of logarithm its maximal term is found. A final condition of the applicability of Ritt's formula to calculate of -order of entire Dirichlet series is established. A necessary and sufficient condition on a function of comparison under which -type of every analytic in the disk function can be expressed by the sequences of modules coefficients of its powers expansion is obtained. All functions of comparison for which -order of every entire function can be expressed by the sequences of modules coefficients of its powers expansion are described. Necessary and sufficient conditions for the existence of Paley effect for entire Dirichlet series with nonnegative coefficients are found.