Information on the thesis

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.
We prove a variant of the uncertainty principle in harmonic analysis for pair
of functions. Problems on decomposition in the Paley-Wiener and weighted
Hardy spaces are considered. We obtain necessary and sufficient conditions of
their solvability. For the Hardy-Smirnov space in unbounded polygonal domains
representation theorem and convolution theorem are obtained.
Key words: analytic function, Hardy space, Smirnov space, cyclic functi-
on, Paley-Wiener space, Paley-Wiener theorem, convolution type equation,
uncertainty principle in harmonic analysis, complete system, minimal system,
Riemann hypothesis.