Browsing by Subject "Analytic functions."

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Factorization in Hardy and Nevanlinna classes
(1999) Gergün, Seçil
We find conditions under which the factors of a function belonging to Hardy or Nevanlinna class also belong to the corresponding class. The basis of our method is the theorem on the representation of a function harmonic in the upper half-plane by Poisson integral under much less restrictive conditions than previously known.
Open Access
On sections and tails of power series
(2002) Zheltukhina, Natalya
The thesis is devoted to the study of connections between properties of a power series and properties of its sections and tails. Power series having sections or tails with multiply positive coefficients are considered and their growth estimates are obtained. Our results strengthen and supplement previous results in this direction, in particular, the well-known P´olya theorem on power series with sections having only negative zeros. The asymptotic zero distribution of linear combinations of sections and tails of the Mittag-Leffler function E1/ρ of order ρ > 1 is studied. Our results generalize and supplement previous results in this direction, in particular, the well-known Szeg¨o result on the linear combinations of sections and tails of the exponential function and the A Edrei, E.B. Saff and R.S. Varga results on sections of E1/ρ.
Open Access
Representations of functions harmonic in the upper half-plane and their applications
(2003) Gergün, Seçil
In this thesis, new conditions for the validity of a generalized Poisson representation for a function harmonic in the upper half-plane have been found. These conditions differ from known ones by weaker growth restrictions inside the halfplane and stronger restrictions on the behavior on the real axis. We applied our results in order to obtain some new factorization theorems in Hardy and Nevanlinna classes. As another application we obtained a criterion of belonging to the Hardy class up to an exponential factor. Finally, our results allowed us to extend the Titchmarsh convolution theorem to linearly independent measures with unbounded support.