Weighted θ-incomplete pluripotential theory

Muhammed Ali Alan. "Weighted θ-incomplete pluripotential theory." Annales Polonici Mathematici 99.2 (2010): 107-128. <http://eudml.org/doc/280160>.

@article{MuhammedAliAlan2010,
abstract = {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)].},
author = {Muhammed Ali Alan},
journal = {Annales Polonici Mathematici},
keywords = {weighted pluripotential theory; -incomplete pluripotential theory; weighted Bergman kernels},
language = {eng},
number = {2},
pages = {107-128},
title = {Weighted θ-incomplete pluripotential theory},
url = {http://eudml.org/doc/280160},
volume = {99},
year = {2010},
}

TY - JOUR
AU - Muhammed Ali Alan
TI - Weighted θ-incomplete pluripotential theory
JO - Annales Polonici Mathematici
PY - 2010
VL - 99
IS - 2
SP - 107
EP - 128
AB - 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)].
LA - eng
KW - weighted pluripotential theory; -incomplete pluripotential theory; weighted Bergman kernels
UR - http://eudml.org/doc/280160
ER -