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Transactions of the American Mathematical Society

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Monge-Ampère measures associated to extremal plurisubharmonic functions in $ {\bf C}\sp n$

Author: Norman Levenberg
Journal: Trans. Amer. Math. Soc. 289 (1985), 333-343
MSC: Primary 32F05
MathSciNet review: 779067
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Abstract: We consider the extremal plurisubharmonic functions $ L_E^\ast $ and $ U_E^\ast $ associated to a nonpluripolar compact subset $ E$ of the unit ball $ B \subset {{\mathbf{C}}^n}$ and show that the corresponding Monge-Ampère measures $ {(d{d^c}L_E^\ast )^n}$ and $ {(d{d^c}U_E^\ast )^n}$ are mutually absolutely continuous. We then discuss the polynomial growth condition $ ({L^\ast})$, a generalization of Leja's polynomial condition in the plane, and study the relationship between the asymptotic behavior of the orthogonal polynomials associated to a measure on $ E$ and the $ ({L^\ast})$ condition.

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