Weighted Bernstein-Markov property in ℂⁿ
We study the weighted Bernstein-Markov property for subsets in ℂⁿ which might not be bounded. An application concerning approximation of the weighted Green function using Bergman kernels is also given.
Weighted pluripotential theory on compact Kähler manifolds
We introduce a weighted version of the pluripotential theory on compact Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behavior under holomorphic maps. We also develop a homogeneous version of the weighted theory and establish a generalization of Siciak's H-principle.
Weighted θ-incomplete pluripotential theory
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...