# Weighted θ-incomplete pluripotential theory

Annales Polonici Mathematici (2010)

- Volume: 99, Issue: 2, page 107-128
- ISSN: 0066-2216

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topMuhammed 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 -

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