Dilnyi V. Asymptotic and approximation properties of functions of exponential type and their applications

In the dissertation paper we consider some spaces of analytic functions, in particular, weighted Hardy spaces with exponential growth of weight. The central result is the criterion for cyclicity of functions in this space. For this result we develop a theory of weighted Hardy spaces, including Paley-Wiener type theorems on representation and on analytic continuation, Phragmen-Lindelof type theorems, as well as Cauchy and Poisson type theorem. These results are used to describe solutions of the convolution type equation in a half-strip, for studies on the Riemann zeta function. For the Hardy-Smirnov space in unbounded polygonal domains representation theorem and convolution theorem are obtained.