Function weighted measures and orthogonal polynomials on Julia sets

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Fekete Polynomials and Shapes of Julia Sets

We prove that a nonempty, proper subset S of the complex plane can be approximated in a strong sense by polynomial filled Julia sets if and only if S is bounded and Ĉ \ int(S) is connected. The proof that such a set is approximable by filled Julia sets is constructive and relies on Fekete polynomials. Illustrative examples are presented. We also prove an estimate for the rate of approximation i...

Constrained Ultraspherical-Weighted Orthogonal Polynomials on Triangle

We construct Ultraspherical-weighted orthogonal polynomials C (λ,γ) n,r (u, v, w), λ > − 2 , γ > −1, on the triangular domain T, where 2λ + γ = 1. We show C (λ,γ) n,r (u, v, w), r = 0, 1, . . . , n; n ≥ 0 form an orthogonal system over the triangular domain T with respect to the Ultraspherical weight function. Mathematics Subject Classification: 33C45, 42C05, 33C70

Jacobi-weighted Orthogonal Polynomials on Triangular Domains

We construct Jacobi-weighted orthogonal polynomials (α,β,γ) n,r (u,v,w), α,β,γ > −1, α+ β + γ = 0, on the triangular domain T . We show that these polynomials (α,β,γ) n,r (u, v,w) over the triangular domain T satisfy the following properties: (α,β,γ) n,r (u,v,w) ∈ n, n≥ 1, r = 0,1, . . . ,n, and (α,β,γ) n,r (u,v,w) ⊥ (α,β,γ) n,s (u,v,w) for r =s. Hence, (α,β,γ) n,r (u,v,w), n= 0,1,2, . . ., r =...

On Generating Orthogonal Polynomials for Discrete Measures