Weighted $\theta$-incomplete pluripotential theory

Muhammed Ali Alan¹

¹ Department of Mathematics Indiana University Bloomington, IN 47405, U.S.A.

Annales Polonici Mathematici, Tome 99 (2010) no. 2, pp. 107-128

Résumé

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)].

Détail

DOI : 10.4064/ap99-2-1

Keywords: weighted pluripotential theory rapidly developing area callaghan ann polon math recently introduced theta incomplete polynomials mathbb paper combine these theories defining weighted theta incomplete pluripotential theory define weighted theta incomplete extremal functions obtain siciak zahariuta type equality terms theta incomplete polynomials finally prove extremal functions recovered using orthonormal polynomials demonstrate result strong asymptotics bergman functions spirit berman indiana univ math