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Positive definite collections of disks
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
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) = -IIk=1n [(z - a(k))((w) over bar - (a) over bar (k)) - R-2]. The main rc-sult of the paper states that in the case when the nodes a(j) are situated at the vertices of a regular n-gon inscribed in the unit circle, the matrix Q (a(i), a(j)) is positive definite if and only if R < rho(n), where z = 2 rho(2)(n) - 1 is the smallest not equal -1 zero of the Jacobi polynomial P-v(n-2v,-1) (z), v = [n/2].

Place, publisher, year, edition, pages
2006. Vol. 55, no 6, 1907-1934 p.
Keyword [en]
positivity, orthogonal polynomials, the Jacobi polynomials
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-37657DOI: 10.1512/iumj.2006.55.3004ISI: 000243513900007Scopus ID: 2-s2.0-33846889998OAI: oai:DiVA.org:kth-37657DiVA: diva2:434665
Available from: 2011-08-16 Created: 2011-08-16 Last updated: 2017-12-08Bibliographically approved

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