| Abstract [eng] |
The periodic Hurwitz zeta-function is a generalization of the classical Hurwitz zeta-function. It is defined by the Dirichlet series depending on a fixed parameter with periodic coefficients. In the thesis, theorems on the approximation of a wide class of analytic functions by shifts of the periodic Hurwitz zeta-function are obtained. Theorems of such a kind are called the universality theorems. Various cases of the parameter are discussed. Moreover, two types of universality, continuous and discrete, are considered. Also, universality theorems for compositions of the periodic Hurwitz zeta-function with operators in the space of analytic functions are obtained, and estimates for number of zeros of considered functions are proved. The used conditions for the parameter are expressed by the linear independence over the field of rational numbers for some infinite sets. Proofs of universality theorems are based on limit theorems of weakly convergent probability measures in the space of analytic functions. |
