2006/01/31 by Julius Borcea
Mathematics · #math.CV #math.CA #msc:30C15 #msc:30C10 #msc:26C10 #msc:12D10
published as Mathematica Scandinavica vol 99:1 (2006), 53-75. · Final version, to appear in Mathematica Scandinavica, 16 pages, no figures, LaTeX2e
arxiv created 2006/05/29 · arxiv updated 2009/12/01
Let S(n,0) be the set of monic complex polynomials of degree n≥ 2 having all their zeros in the closed unit disk and vanishing at 0. For p∈ S(n,0) denote by |p|0 the distance from the origin to the zero set of p'. We determine all 0-maximal polynomials of degree n, that is, all polynomials p∈ S(n,0) such that |p|0≥ |q|0 for any q∈ S(n,0). 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.