Zeros of the derivatives of Faber polynomials associated with a universal covering map

0Citations
Citations of this article
2Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

For a compact set E ⊂ C with connected complement, we study asymptotic behavior of normalized zero counting measures { μk } of the derivatives of Faber polynomials associated with E. For example if E has empty interior, we prove that { μk } converges in the weak-star topology to a probability measure whose support is the boundary of g (D), where g : { | z | > r } ∪ { ∞ } → over(C, -) {minus 45 degree rule} E is a universal covering map such that g (∞) = ∞ and D is the Dirichlet domain associated with g and centered at ∞. Our results are counterparts of those of Kuijlaars and Saff [Asymptotic distribution of the zeros of Faber polynomials, Math. Proc. Cambridge Philos. Soc. 118 (1995) 437-447] on zeros of Faber polynomials. © 2006 Elsevier Inc. All rights reserved.

Cite

CITATION STYLE

APA

Oh, B. G. (2007). Zeros of the derivatives of Faber polynomials associated with a universal covering map. Journal of Approximation Theory, 145(1), 1–19. https://doi.org/10.1016/j.jat.2006.06.005

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free