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## Weighted $\theta$-incomplete pluripotential theory

### Tom 99 / 2010

Annales Polonici Mathematici 99 (2010), 107-128 MSC: Primary 32U35. DOI: 10.4064/ap99-2-1

#### Streszczenie

Weighted pluripotential theory is a rapidly developing area; and Callaghan [Ann. Polon. Math. 90 (2007)] recently introduced $\theta$-incomplete polynomials in $\mathbb C$ for $n>1$. 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 Berman [Indiana Univ. Math. J. 58 (2009)].

#### Autorzy

• Muhammed Ali AlanDepartment of Mathematics
Indiana University
Bloomington, IN 47405, U.S.A.
e-mail

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