Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem
| dc.creator | Malamud, S. M. | |
| dc.date | 2003-04-12 | |
| dc.date | 2003-07-06 | |
| dc.date.accessioned | 2026-07-07T04:56:48Z | |
| dc.date.available | 2026-07-07T04:56:48Z | |
| dc.description | We estabish an analog of the Cauchy-Poincare separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borg-type result) for a normal matrix. Using this result we essentially generalize and complement the known Gauss--Lucas theorem on the geometry of the roots of a complex polynomial and of its derivative. In turn the last result is applied to prove the old conjectures of de Bruijn-Springer and Schoenberg about these roots. | |
| dc.description | typos corrected; references added | |
| dc.identifier | https://arxiv.org/abs/math/0304158 | |
| dc.identifier | http://arxiv.org/abs/math/0304158 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67058 | |
| dc.subject | Complex Variables | |
| dc.subject | Spectral Theory | |
| dc.subject | 15A29; 30C10; 30C15 | |
| dc.title | Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem | |
| dc.type | text |