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

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On_the_poisson_representation_of_a_function_harmonic_in_the_upper_half_plane.pdf (255.81 KB)

Date

2002

Authors

Gergün, S.
Ostrovskii, I.

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Source Title

Computational Methods and Function Theory

Print ISSN

1617-9447

Electronic ISSN

2195-3724

Publisher

Springer

Volume

2

Issue

1

Pages

191 - 213

Language

English

Type

Article

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Abstract

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.

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Keywords

Compactness, Green function, Nevanlinna formula, Phragmen - Lindel of Principle, Poisson integral, Subharmonic function

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http://hdl.handle.net/11693/48794

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Scholarly Publications - Mathematics