Computational Methods and Function Theory 2 (2002), No. 1, 191--213
Copyright Heldermann Verlag 2002
Seçil Gergün
gergun@fen.bilkent.edu.tr, Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey.
Iossif V. Ostrovskii
iossif@fen.bilkent.edu.tr, Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey; Institute for Low Temperature Physics and Engineering, 47 Lenin ave, 61103 Kharkov, Ukraine.
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.
Keywords: Compactness, Green function, Nevanlinna formula, Phragmén-Lindelöf Principle, Poisson integral, subharmonic function.
MSC 2000: 31A05, 31A10.
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