Weighted pluripotential theory is a rapidly developing area; and Callaghan [Ann. Polon. Math. 90 (2007)] recently introduced θ-incomplete polynomials in ℂ for n>1. In this paper we combine these two theories by defining weighted θ-incomplete pluripotential theory. We define weighted θ-incomplete extremal functions and obtain a Siciak-Zahariuta type equality in terms of θ-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)].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-1,
author = {Muhammed Ali Alan},
title = {Weighted $\theta$-incomplete pluripotential theory},
journal = {Annales Polonici Mathematici},
volume = {98},
year = {2010},
pages = {107-128},
zbl = {1217.32013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-1}
}
Muhammed Ali Alan. Weighted θ-incomplete pluripotential theory. Annales Polonici Mathematici, Tome 98 (2010) pp. 107-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap99-2-1/