Abstract.
We consider (pluricomplex) Green functions defined on \({\mathbb C}^n\), with logarithmic poles in a finite set and with logarithmic growth at infinity. For certain sets, we describe all the corresponding Green functions. The set of these functions is large and it carries a certain algebraic structure. We also show that for some sets no such Green functions exist. Our results indicate the fact that the set of poles should have certain algebro-geometric properties in order for these Green functions to exist.
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Received November 24, 1998; in final form April 19, 1999 / Published online July 3, 2000
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Coman, D. Certain classes of pluricomplex Green functions on ${\mathbb C}^n$. Math Z 235, 111–122 (2000). https://doi.org/10.1007/s002090000126
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DOI: https://doi.org/10.1007/s002090000126