Weighted $θ$-Incomplete Pluripotential Theory

Details Weighted $θ$-Incomplete Pluripotential Theory Weighted $θ$-Incomplete Pluripotential Theory

2008-10-20

arxiv.org/abs/0810.3450v2

Mathematics

Complex Variables

27 Pages, A new theorem added, Some corrections made

Scientific paper

Weighted pluripotential theory is a rapidly developing area; and Callaghan \cite{Callaghan} recently introduced $\theta$-incomplete polynomials in \cd for $d>1$. In this paper we combine these two theories by defining weighted $\theta$-incomplete pluripotential theory. We define weighted $\theta$-incomplete extremal functions and obtain a Siciak-Zahariuta type equality in terms of $\theta$-incomplete polynomials. Finally we prove that the extremal functions can be recovered using orthonormal polynomials and we demonstrate a result on strong asymptotics of Bergman functions in the spirit of \cite{BermanCn}.

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