A generalization of the Gauss-Lucas theorem |
| |
| Authors: | J L Díaz-Barrero J J Egozcue |
| |
| Institution: | (1) Applied Mathematics III, Universitat Politècnica de Catalunya, Jordi Girona 1-3, C2, 080 34 Barcelona, Spain |
| |
| Abstract: | Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros
except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives
is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations
of incomplete polynomials is also given. |
| |
| Keywords: | polynomials location of zeros convex hull of the zeros Gauss-Lucas theorem |
| 本文献已被 SpringerLink 等数据库收录！ |
