Spectral order and isotonic differential operators of Laguerre-Polya type
| dc.creator | Borcea, Julius | |
| dc.date | 2004-04-19 | |
| dc.date | 2006-01-21 | |
| dc.date.accessioned | 2026-07-07T08:18:37Z | |
| dc.date.available | 2026-07-07T08:18:37Z | |
| dc.description | The spectral order on $\bR^n$ induces a natural partial ordering on the manifold $\calH_{n}$ of monic hyperbolic polynomials of degree $n$. We show that all differential operators of Laguerre-Pólya type preserve the spectral order. We also establish a global monotony property for infinite families of deformations of these operators parametrized by the space $\li$ of real bounded sequences. As a consequence, we deduce that the monoid $\calA'$ of linear operators that preserve averages of zero sets and hyperbolicity consists only of differential operators of Laguerre-Pólya type which are both extensive and isotonic. In particular, these results imply that any hyperbolic polynomial is the global minimum of its $\calA'$-orbit and that Appell polynomials are characterized by a global minimum property with respect to the spectral order. | |
| dc.description | Final version, to appear in Ark. Mat.; 21 pages, no figures, LaTeX2e | |
| dc.identifier | https://arxiv.org/abs/math/0404336 | |
| dc.identifier | http://arxiv.org/abs/math/0404336 | |
| dc.identifier | Ark. Mat. 44 (2006), 211-240. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/134494 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | Primary 47D06; Secondary 26C05, 30C15, 47B60 | |
| dc.title | Spectral order and isotonic differential operators of Laguerre-Polya type | |
| dc.type | text |