Integral Representation of Harmonic Function in a Half-Plane
Received:April 09, 2007  Revised:July 13, 2007
Key Words: integral representation   harmonic functions   modified Poisson kernel.  
Fund Project:the National Natural Science Foundation of China (No.10671022); Research Foundation for Doctor Programme (No.20060027023); Henan Institute of Education Youth Scientific Research Fund (No.20070107).
Author NameAffiliation
LI Hong Wei Mathematics Department, Henan Institute of Education, Henan 450014, China
Sch. Math. Sci. \& Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China 
DENG Guan Tie Sch. Math. Sci. \& Lab. Math. Com. Sys., Beijing Normal University, Beijing 100875, China 
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Abstract:
      In this article, we consider the integral representation of harmonic functions. Using a property of the modified Poisson kernel in a half plane, we prove that a harmonic function $u(z)$ in a half plane with its positive part $u^ (z)=\max\{u(z),0\}$ satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.
Citation:
DOI:10.3770/j.issn:1000-341X.2009.04.011
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