Publication: On the roots of generalized Wills μ-polynomials
Authors
Hernández Cifre, María de los Ángeles ; Yepes Nicolás, Jesús
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Facultad de Matemáticas
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Publisher
EMS Press
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DOI
https://doi.org/10.4171/RMI/842
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info:eu-repo/semantics/article
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.
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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
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