Computing the Pluricomplex Green Function with Two Poles

Computing the Pluricomplex Green Function with Two Poles

Convergence in Capacity of the Pluricomplex Green Function

In this paper we prove that if Ω is a bounded hyperconvex domain in C and if Ω 3 zj → ∂Ω, j → ∞, then the pluricomplex Green function gΩ(zj , ·) tends to 0 in capacity, as j →∞. A bounded open connected set Ω ⊂ Cn is called hyperconvex if there exists negative plurisubharmonic function ψ ∈ PSH(Ω) such that {z ∈ Ω : ψ(z) < c} ⊂⊂ Ω for all c < 0. Such ψ is called an exhaustion function for Ω. It ...

Rational Function Computing with Poles and Residues

Computer algebra systems (CAS) usually support computation with exact or approximate rational functions stored as ratios of polynomials in “expanded form” with explicit coefficients. We examine the consequences of using a partial-fraction type of form in which all rational functions are expressed as a polynomial plus a sum of terms each of which has a denominator consisting of a monic univariat...

On the Regularity of the Pluricomplex Green Functions

Computing orthogonal rational functions with poles near the boundary

Computing orthogonal rational functions is a far from trivial problem, especially for poles close to the boundary of the support of the orthogonality measure. In this paper we analyze some of the difficulties involved and present two different approaches to solve this problem.