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Monge-Ampère Measures Associated to Extremal Plurisubharmonic Functions in Cn
Transactions of the American Mathematical Society
Vol. 289, No. 1 (May, 1985), pp. 333-343
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/1999703
Page Count: 11
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We consider the extremal plurisubharmonic functions L* E and U* E associated to a nonpluripolar compact subset E of the unit ball $B \subset C^n$ and show that the corresponding Monge-Ampère measures (ddcL * E)n and (ddcU * E)n are mutually absolutely continuous. We then discuss the polynomial growth condition (L*), 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*) condition.
Transactions of the American Mathematical Society © 1985 American Mathematical Society