62 research outputs found
Maximal and linearly inextensible polynomials
Let S(n,0) be the set of monic complex polynomials of degree having
all their zeros in the closed unit disk and vanishing at 0. For
denote by the distance from the origin to the zero set of . We
determine all 0-maximal polynomials of degree , that is, all polynomials
such that for any . Using a
second order variational method we then show that although some of these
polynomials are linearly inextensible, they are not locally maximal for
Sendov's conjecture.Comment: Final version, to appear in Mathematica Scandinavica, 16 pages, no
figures, LaTeX2
Hyperbolicity preservers and majorization
The majorization order on \RR^n induces a natural partial ordering on the
space of univariate hyperbolic polynomials of degree . We characterize all
linear operators on polynomials that preserve majorization, and show that it is
sufficient (modulo obvious degree constraints) to preserve hyperbolicity.Comment: 4 pages, Published as C. R. Math. Acad. Sci. Paris 348 (2010),
843-84
- …