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Positive definite collections of disks
Volgograd State University, Russia.ORCID iD: 0000-0002-8422-6140
2006 (English)In: Indiana University Mathematics Journal, ISSN 0022-2518, E-ISSN 1943-5258, Vol. 55, no 6, 1907-1934 p.Article in journal (Refereed) Published
Abstract [en]

Let Q(z,w)=−∏k=1n[(z−ak)(w¯−a¯k)−R2]. The main result of the paper states that in the case when the nodes ajare situated at the vertices of a regular n-gon inscribed in the unit circle, the matrix Q(ai,aj)is positive definite if and only if R<ρn, where z=2ρn2−1is the smallest ≠−1zero of the Jacobi polynomial Pνn−2ν,−1(z), ν=[n/2].

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Place, publisher, year, edition, pages
2006. Vol. 55, no 6, 1907-1934 p.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-79624DOI: 10.1512/iumj.2006.55.3004OAI: oai:DiVA.org:liu-79624DiVA: diva2:607577
Available from: 2013-02-25 Created: 2012-08-11 Last updated: 2017-12-06

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Tkachev, Vladimir

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