Information on the thesis

The thesis consists of a list of denotations, introduction, 4 chapters divided
into sections, conclusions and a bibliography, which includes 106 items.
In Chapter 1 we introduce an overview of works related to Hardy spaces and
formulate the main results of the thesis.
In Chapter 2 of the dissertation paper we consider relationships between
properties of functions in Hardy-type spaces and the behavior of functions insi-
de the domain of analyticity. We obtain existence theorems and uniqueness
theorems in weighted Hardy spaces.
In Chapter 3 the description of the translation invariant subspaces of wei-
ghted Hardy spaces is supplemented. We showed the equivalence of the rapid
growth in some sense on imaginary axis and rapid decrease on the positive
half-axis for functions in the space H^∞_σ.
We describe the properties of the space defined by the intersections of weighted Hardy spaces.
In Chapter 3 for the decomposition problem in Paley-Wiener space W¹_σ
we found the new way of splitting and obtain the solvability criterion.
These results can be used as in further investigations inside the theory of
functions, and in other directions of mathematics.
Key words: analytic function, Hardy space, uniqueness theorem, cyclic
function, Paley-Wiener space, decomposition problem.