Seçil Gergün, I. V. Ostrovskii, “On the Poisson representation of a function harmonic in the upper half-plane”, Mat. Fiz. Anal. Geom., 2002, Volume 9, Number 2,Pages <nobr>243

This article is cited in 1 paper

On the Poisson representation of a function harmonic in the upper half-plane

Seçil Gergün^a, I. V. Ostrovskii^ba

^a Department of Mathematics, Bilkent University, 06533 Bilkent, Ankara, Turkey
^b Mathematics Division, B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov, 61103, Ukraine

Abstract: New conditions of 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 in the neighbourhood of the real axis.

MSC: 31A05, 31A10

Received: 21.11.2001

Language: English