Browsing by Subject "Subharmonic function"

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    On a Problem of A. Eremenko
    (Springer, 2005-05) Ostrovskii, I. V.
    Let Pmn, 0 < m < n− 1, be a polynomial formed by the first m terms of the expansion of (1 + z)n according to the binomial formula. We show that, if m, n→∞ in such a way that limm,n→∞ m/n = α ∈ (0, 1), then the zeros of Pmn tend to a curve which can be explicitly described.
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    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.