On the roots of generalized Wills μ-polynomials

Hernández Cifre, María de los Ángeles; Yepes Nicolás, Jesús

Publication:
On the roots of generalized Wills μ-polynomials

dc.contributor.author	Hernández Cifre, María de los Ángeles
dc.contributor.author	Yepes Nicolás, Jesús
dc.contributor.department	Matemáticas
dc.contributor.other	Facultad de Matemáticas
dc.date.accessioned	2026-02-25T17:38:16Z
dc.date.available	2026-02-25T17:38:16Z
dc.date.issued	2015-07-16
dc.description.abstract	We investigate the roots of a family of geometric polynomials of convex bodies associated to a given measure μ on the non-negative real line R>=0, which arise from the so called Wills functional. We study its structure, showing that the set of roots in the upper half-plane is a closed convex cone, containing the non-positive real axis R>=0, and strictly increasing in the dimension, for any measure μ. Moreover, it is proved that the "smallest" cone of roots of these μ-polynomials is the one given by the Steiner polynomial, which provides, for example, additional information about the roots of μ-polynomials when the dimensión is large enough. It will also give geometric necessary conditions for a sequence {m_i : i = 0, 1,....} to be the moments of a certain measure on R>=0, a question regarding the so called (Stieltjes) moment problem.
dc.format	application/pdf
dc.format.extent	19
dc.identifier.citation	María A. Hernández Cifre, Jesús Yepes Nicolás, On the roots of generalized Wills μ-polynomials. Rev., Mat. Iberoam. 31 (2015), no. 2, pp. 477–496
dc.identifier.doi	https://doi.org/10.4171/RMI/842
dc.identifier.eissn	2235-0616
dc.identifier.issn	0213-2230
dc.identifier.uri	http://hdl.handle.net/10201/213623
dc.language	eng
dc.publisher	EMS Press
dc.relation	Supported by MINECO-FEDER project MTM2012-34037 and by “Programa de Ayudas a Grupos de Excelencia de la Región de Murcia”, Fundación Séneca, 04540/GERM/06.
dc.relation.publisherversion	https://ems.press/journals/rmi/articles/13277
dc.rights	Attribution 4.0 International	*
dc.rights.accessRights	info:eu-repo/semantics/openAccess
dc.rights.uri	http://creativecommons.org/licenses/by/4.0/	*
dc.subject	Generalized Wills functional
dc.subject	Location of roots
dc.subject	Weighted Steiner polynomial
dc.subject	Measures
dc.subject	Stieltjes moment problem
dc.subject.ods	No relacionado con ningún objetivo de desarrollo sostenible
dc.title	On the roots of generalized Wills μ-polynomials
dc.type	info:eu-repo/semantics/article
dc.type.version	info:eu-repo/semantics/acceptedVersion
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