| Abstract [eng] |
In the thesis, universality theorems on the approximation of analytic functions in the strip D by shifts of the periodic zeta-function are obtained. For a periodic sequence of complex numbers with minimal period q the periodic zeta-function is defined by the Dirichlet series and have a meromorphic continuation to the whole complex plane. In the thesis, it is proved that with certain conditions inequality of universality for periodic zeta-function holds. If one member of the sequence is certain combination of other members then periodic zeta-function is universal with certain conditions. If the weight function is satisfying certain conditions, and the sequence is multiplicative, inequality of weighted universality holds. In weighted discrete universality theorems of periodic zeta-function in approximating shifts takes values from the arithmetic progression or from a more complicated discrete set. In the thesis is proved that inequality of joint universality for periodic zeta-function holds with certain conditions. For the composition from the Lipschitz class, the universality theorem in the thesis also is proved, and certain bound of number of zeros of this function is obtained. |
