Maximal and linearly inextensible polynomials

dc.creatorBorcea, Julius
dc.date2006-01-25
dc.date2006-05-29
dc.date.accessioned2026-07-07T07:43:51Z
dc.date.available2026-07-07T07:43:51Z
dc.descriptionLet S(n,0) be the set of monic complex polynomials of degree $n\ge 2$ having all their zeros in the closed unit disk and vanishing at 0. For $p\in S(n,0)$ denote by $|p|_{0}$ the distance from the origin to the zero set of $p'$. We determine all 0-maximal polynomials of degree $n$, that is, all polynomials $p\in S(n,0)$ such that $|p|_{0}\ge |q|_{0}$ for any $q\in S(n,0)$. Using a second order variational method we then show that although some of these polynomials are linearly inextensible, they are not locally maximal for Sendov's conjecture.
dc.descriptionFinal version, to appear in Mathematica Scandinavica, 16 pages, no figures, LaTeX2e
dc.identifierhttps://arxiv.org/abs/math/0601600
dc.identifierhttp://arxiv.org/abs/math/0601600
dc.identifierMathematica Scandinavica vol 99:1 (2006), 53-75.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122988
dc.subjectComplex Variables
dc.subjectClassical Analysis and ODEs
dc.subjectPrimary: 30C15; Secondary: 30C10, 26C10, 12D10
dc.titleMaximal and linearly inextensible polynomials
dc.typetext

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