Inequalities for products of polynomials I - Pritsker, I.E.; Ruscheweyh, S. (MATHEMATICA SCANDINAVICA, 2009)
We study inequalities connecting the product of uniform norms of polynomials with the norm of their product. This circle of problems include the Gelfond-Mahler inequality for the unit disk and the Kneser-Borwein inequality for the segment [-1,1]. Furthermore, the asymptotically sharp constants are known for such inequalities over arbitrary compact sets in the complex plane. It is shown here that this best constant is smallest (namely: 2) for a disk. We also conjecture that it takes its largest value for a segment, among all compact connected sets in the plane.