Maximal and linearly inextensible polynomials
| dc.creator | Borcea, Julius | |
| dc.date | 2006-01-25 | |
| dc.date | 2006-05-29 | |
| dc.date.accessioned | 2026-07-07T07:43:51Z | |
| dc.date.available | 2026-07-07T07:43:51Z | |
| dc.description | Let 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.description | Final version, to appear in Mathematica Scandinavica, 16 pages, no figures, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/0601600 | |
| dc.identifier | http://arxiv.org/abs/math/0601600 | |
| dc.identifier | Mathematica Scandinavica vol 99:1 (2006), 53-75. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/122988 | |
| dc.subject | Complex Variables | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Primary: 30C15; Secondary: 30C10, 26C10, 12D10 | |
| dc.title | Maximal and linearly inextensible polynomials | |
| dc.type | text |