Convexity properties of twisted root maps
| dc.creator | Borcea, Julius | |
| dc.date | 2003-12-17 | |
| dc.date | 2007-10-20 | |
| dc.date.accessioned | 2026-07-07T09:53:00Z | |
| dc.date.available | 2026-07-07T09:53:00Z | |
| dc.description | The strong spectral order induces a natural partial ordering on the manifold $H_{n}$ of monic hyperbolic polynomials of degree $n$. We prove that twisted root maps associated with linear operators acting on $H_{n}$ are Gårding convex on every polynomial pencil and we characterize the class of polynomial pencils of logarithmic derivative type by means of the strong spectral order. Let $A'$ be the monoid of linear operators that preserve hyperbolicity as well as root sums. We show that any polynomial in $H_{n}$ is the global minimum of its $A'$-orbit and we conjecture a similar result for complex polynomials. | |
| dc.description | final version, to appear in Rocky Mountain J. Math.; 14 pages, no figures, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/0312321 | |
| dc.identifier | http://arxiv.org/abs/math/0312321 | |
| dc.identifier | Rocky Mountain J. Math. 38 (2008), 809-834 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/165798 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 39B62 (Primary) 26C10, 30C15, 60E15 (Secondary) | |
| dc.title | Convexity properties of twisted root maps | |
| dc.type | text |