Browsing by Subject "Poisson integral"

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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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    ItemOpen Access
    On the Poisson representation of a function harmonic in the upper half-plane
    (Springer, 2002) Gergün, S.; Ostrovskii, I.
    New conditions for the validity of the Poisson representation (in usual and generalized form) for a function harmonic in the upper half-plane are obtained. These conditions differ from known ones by weaker growth restrictions inside the half-plane and stronger restrictions on the behavior on the real axis.