Some Extreme Rays of the Positive Pluriharmonic Functions
Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 9-16
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1.1. We will denote by B the open unit ball in C n , and we will denote by H(B) the class of all holomorphic functions on B. Let Thus N(B) is convex (and compact in the compact open topology). We think that the structure of N(B) is of interest and importance. Thus we proved in [1] that if (1.1) if (1.2) and if n≧ 2, then g is an extreme point of N(B). We will denote by E(B) the class of all extreme points of N(B). If n = 1 and if (1.2) holds, then as is well known g ∈ E(B) if and only if (1.3)
Forelli, Frank. Some Extreme Rays of the Positive Pluriharmonic Functions. Canadian journal of mathematics, Tome 31 (1979) no. 1, pp. 9-16. doi: 10.4153/CJM-1979-002-1
@article{10_4153_CJM_1979_002_1,
author = {Forelli, Frank},
title = {Some {Extreme} {Rays} of the {Positive} {Pluriharmonic} {Functions}},
journal = {Canadian journal of mathematics},
pages = {9--16},
year = {1979},
volume = {31},
number = {1},
doi = {10.4153/CJM-1979-002-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1979-002-1/}
}
[1] 1. Forelli, F., Measures whose Poisson integrals are pluriharmonic II, Illinois J. Math. 19 (1975), 584–592. Google Scholar
[2] 2. Forelli, F., A necessary condition on the extreme points of a class of holomorphic functions, Pacific J. Math. 73 (1977), 81–86. Google Scholar
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