Geodesic
Ray sequences of Laurent-type rational functions
Electronic transactions on numerical analysis, Tome 4 (1996), pp. 106-124.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: This paper is devoted to the study of asymptotic zero distribution of Laurent-type approximants under certain extremality conditions analogous to the condition of Grothmann [1], which can be traced back to Walsh's theory of exact harmonic majorants [8, 9]. We also prove results on the convergence of ray sequences of Laurent-type approximants to a function analytic on the closure of a finitely connected Jordan domain and on the zero distribution of optimal ray sequences. Some applications to the convergence and zero distribution of the best Lp approximants are given. The arising theory is similar to Walsh's theory of maximally convergent polynomials to a function in a simply connected domain [10].
Classification : 30E10, 30C15, 41A20, 31A15
Keywords: Laurent-type rational functions, zero distributions, convergence, optimal ray sequences, best lp approximants 
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     author = {Pritsker, I.E.},
     title = {Ray sequences of {Laurent-type} rational functions},
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     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_1996__4__a3/}
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Pritsker, I.E. Ray sequences of Laurent-type rational functions. Electronic transactions on numerical analysis, Tome 4 (1996), pp. 106-124. http://geodesic.mathdoc.fr/item/ETNA_1996__4__a3/