Information on the thesis

The thesis for obtaining the Candidate of Physical and Mathematical Sciences degree on the speciality   01.01.01 — mathematical analysis. — Ivan Franko Lviv National University, Lviv, 2015.

In this thesis a counterpart of Jensen- Littlewood lemma for meromorphic functions f in a closure of the half-strip S = {σ + it:σ>0, 0 <t<2π}, such that f(σ)= f(σ+2πi), is proved. The Nevanlinna characteristic for such functions is introduced, and its main properties are investigated. The relations for the Fourier coefficients of the logarithm modulus of meromorphic function in the closure of the rectangle R_η={σ + it:σ>0, 0 <σ<η, 0 <t<2π} are investigated, which helped to formulate and prove a criterion of λ-type finiteness of holomorphic in the half-strip functions in terms of Fourier coefficient of  log|f|  and describe the zero sets of holomorphic and zero and pole sets of meromorphic functions f  of finite λ-type with arbitrary restrictions on their growth characteristics. A counterpart of the Jensen formula and the main properties of Nevanlinna characteristic T₀(r, F) of meromorphic function in the exterior of the unit disk are proved. A criterion of λ-type finiteness of holomorphic in the exterior of the unit disk functions F  in terms of Fourier coefficients of log|F| is obtained. The comparison between T₀(r, F) and the classical Nevanlinna characteristic T(r, F) for functions which allow the meromorphic continuation into C is done. Zero sets of holomorphic and pole sets of meromorphic functions of finite λ-type in the exterior of the unit disk are described. The asymptotic for Nevanlinna characteristic of loxodromic functions is obtained. The classes M_q of multiplicatively periodic meromorphic functions in the punctured closure of the upper half-plane is introduced. A value distribution theorem for functions from M_q is proved.

Key words: holomorphic function, meromorphic function, function of finite λ-type, multiplicatively periodic meromorphic function, loxodromic function,

Jensen-Littlewood lemma, Nevanlinna characteristic, sequence of finite λ-density, λ-admissible sequence.