Asymptotic Zero Distribution of Laurent-Type Rational Functions
Date
1997Author
Papamichael, NicolasPritsker, I. E.
Saff, E. B.
Source
Journal of Approximation TheoryVolume
89Issue
1Pages
58-88Google Scholar check
Metadata
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We study convergence and asymptotic zero distribution of sequences of rational functions with fixed location of poles that approximate an analytic function in a multiply connected domain. Although the study of zero distributions of polynomials has a long history, analogous results for truncations of Laurent series have been obtained only recently by Edrei (Michigan Math. J.29(1982), 43-57). We obtain extensions of Edrei's results for more general sequences of Laurent-type rational functions. It turns out that the limiting measure describing zero distributions is a linear convex combination of the harmonic measures at the poles of rational functions, which arises as the solution to a minimum weighted energy problem for a special weight. Applications of these results include the asymptotic zero distribution of the best approximants to analytic functions in multiply connected domains, Faber-Laurent polynomials, Laurent-Padé approximants, trigonometric polynomials, etc. © 1997 Academic Press.