Abstract.
Let Ω be a domain in the extended complex plane such that ∞∈Ω . Further, let K= C / Ω and, for each n , let Q n be a monic polynomial of degree n with all its zeros in K . This paper is concerned with whether (Q n ) can be chosen so that, if f is any holomorphic function on Ω and P n is the polynomial part of the Laurent expansion of Q n f at ∞ , then (P n /Q n ) converges to f locally uniformly on Ω . It is shown that such a sequence (Q n ) can be chosen if and only if either K has zero logarithmic capacity or Ω is regular.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
January 21, 1999. Date accepted: August 17, 1999.
Rights and permissions
About this article
Cite this article
Gardiner, S. Convergence of Rational Interpolants with Preassigned Poles. Constr. Approx. 17, 139–146 (2001). https://doi.org/10.1007/s003650010007
Published:
Issue Date:
DOI: https://doi.org/10.1007/s003650010007