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A refinement for rational functions of Polya's method to construct Voronoi diagrams
Stockholm University, Faculty of Science, Department of Mathematics.
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 2
2017 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 452, no 1, 312-334 p.Article in journal (Refereed) Published
Abstract [en]

Given a complex polynomial P with zeroes z(1),..., z(d), we show that the asymptotic zero-counting measure of the iterated derivatives Q((n)), n = 1, 2,..., where Q = R/P is any irreducible rational function, converges to an explicitly constructed probability measure supported by the Voronoi diagram associated with z(1),...,z(d). This refines Polya's Shire theorem for these functions. In addition, we prove a similar result, using currents, for Voronoi diagrams associated with generic hyperplane configurations in C-m.

Place, publisher, year, edition, pages
2017. Vol. 452, no 1, 312-334 p.
Keyword [en]
Zeroes of polynomial, Rational functions: asymptotic measures
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-142356DOI: 10.1016/j.jmaa.2017.02.071ISI: 000398645800018OAI: oai:DiVA.org:su-142356DiVA: diva2:1093399
Available from: 2017-05-05 Created: 2017-05-05 Last updated: 2017-05-05Bibliographically approved

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Bögvad, RikardHägg, Christian
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