Browsing by Subject "Nevanlinna class"

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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.
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    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.