Hyperbolic polynomials and spectral order
| dc.creator | Borcea, Julius | |
| dc.creator | Shapiro, Boris | |
| dc.date | 2003-04-11 | |
| dc.date | 2003-06-04 | |
| dc.date.accessioned | 2026-07-07T04:56:47Z | |
| dc.date.available | 2026-07-07T04:56:47Z | |
| dc.description | The spectral order on $\bR$ induces a partial ordering on the manifold $\calH_{n}$ of monic hyperbolic polynomials of degree $n$. We show that the semigroup $\tilde{\calS}$ generated by differential operators of the form $(1-\la \frac{d}{dx})e^{\la \frac{d}{dx}}$, $\la \in \bR$, acts on the poset $\calH_{n}$ in an order-preserving fashion. We also show that polynomials in $\calH_{n}$ are global minima of their respective $\tilde{\calS}$-orbits and we conjecture that a similar result holds even for complex polynomials. Finally, we show that only those pencils of polynomials in $\calH_{n}$ which are of logarithmic derivative type satisfy a certain local minimum property for the spectral order. | |
| dc.description | The only relevant changes concern the acknowledgements | |
| dc.identifier | https://arxiv.org/abs/math/0304145 | |
| dc.identifier | http://arxiv.org/abs/math/0304145 | |
| dc.identifier | C. R. Math. Acad. Sci. Paris 337 (2003), 693-698 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67048 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Complex Variables | |
| dc.subject | 30C15; 60E15 | |
| dc.title | Hyperbolic polynomials and spectral order | |
| dc.type | text |