Monge-Ampère measures associated to extremal plurisubharmonic functions in $\textbf {C}^ n$
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- by Norman Levenberg PDF
- Trans. Amer. Math. Soc. 289 (1985), 333-343 Request permission
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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 289 (1985), 333-343
- MSC: Primary 32F05
- DOI: https://doi.org/10.1090/S0002-9947-1985-0779067-3
- MathSciNet review: 779067