TY - JOUR
T1 - Extremal positive pluriharmonic functions on euclidean balls
AU - Jafari, Farhad
AU - Putinar, Mihai
PY - 2010/10
Y1 - 2010/10
N2 - Contrary to the well understood structure of positive harmonic functions in the unit disk, most of the properties of positive pluriharmonic functions in symmetric domains of Cn, in particular the unit ball, remain mysterious. In particular, in spite of efforts spread over quite a few decades, no characterization of the extremal rays in the cone of positive pluriharmonic functions in the unit ball of Cn is known. We investigate this question by a geometric tomography technique, and provide some new classes of examples of such extremal functions.
AB - Contrary to the well understood structure of positive harmonic functions in the unit disk, most of the properties of positive pluriharmonic functions in symmetric domains of Cn, in particular the unit ball, remain mysterious. In particular, in spite of efforts spread over quite a few decades, no characterization of the extremal rays in the cone of positive pluriharmonic functions in the unit ball of Cn is known. We investigate this question by a geometric tomography technique, and provide some new classes of examples of such extremal functions.
KW - Ex-tremal measure
KW - Pluriharmonic function
KW - Poisson transform
KW - Riesz-herglotz representation
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U2 - 10.4310/pamq.2010.v6.n4.a3
DO - 10.4310/pamq.2010.v6.n4.a3
M3 - Article
AN - SCOPUS:79952256157
SN - 1558-8599
VL - 6
SP - 1013
EP - 1025
JO - Pure and Applied Mathematics Quarterly
JF - Pure and Applied Mathematics Quarterly
IS - 4
ER -