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MAXIMAL UNIVALENT DISKS OF REAL RATIONAL FUNCTIONS AND HERMITE-BIEHLER POLYNOMIALS
Stockholm University, Faculty of Science, Department of Mathematics.
2011 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 139, no 5, 1625-1635 p.Article in journal (Refereed) Published
Abstract [en]

The well-known Hermite-Biehler theorem claims that a univariate monic polynomial s of degree k has all roots in the open upper half-plane if and only if s = p + iq, where p and q are real polynomials of degree k and k - 1 respectively with all real, simple and interlacing roots, and q has a negative leading coefficient. Considering roots of p as cyclically ordered on RP1 we show that the open disk in CP1 having a pair of consecutive roots of p as its diameter is the maximal univalent disk for the function R = q/p. This solves a special case of the so-called Hermite-Biehler problem.

Place, publisher, year, edition, pages
2011. Vol. 139, no 5, 1625-1635 p.
Keyword [en]
univalent functions, Hermite-Biehler theorem
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-49779ISI: 000290511400011OAI: oai:DiVA.org:su-49779DiVA: diva2:379435
Available from: 2010-12-31 Created: 2010-12-17 Last updated: 2017-12-11Bibliographically approved

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http://arxiv.org/abs/1005.1596v1

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CiteExportLink to record
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