| Abstract [eng] |
This dissertation delves into the approximation of analytic functions using a specific type of series known as Dirichlet series. In particular, the research focuses on periodic zeta functions and their truncated versions. The central goal is to explore the properties of these functions and their potential applications in approximating various analytic functions. By employing a combination of analytic and probabilistic methods, the author establishes a significant result: the universality of these Dirichlet series. This means that by shifting these series in certain ways, they can approximate a wide range of analytic functions. This universality property is a crucial discovery in the field of analytic function approximation. One of the novel aspects of this research is the use of absolutely convergent Dirichlet series. This type of series has specific convergence properties that make them particularly suitable for approximation purposes. The author extends existing universality results to encompass these absolutely convergent Dirichlet series, broadening the scope of functions that can be approximated. Furthermore, the dissertation contributes to the understanding of joint universality. This concept involves approximating multiple functions simultaneously using a single series. The author investigates the joint universality of pairs of Dirichlet series, providing insights into the interplay between these functions and their approximation capabilities. |
