Norms of products and factors polynomials
Abstract
We study inequalities connecting a product of uniform norms of polynomials with the norm of their product. Generalizing Gel’fond-Mahler inequality for the unit disk and Kneser-Borwein inequality for the segment [−1,1], we prove an asymptotically sharp inequality for norms of products of algebraic polynomials over an arbitrary compact set in plane. Applying similar techniques, we produce a related inequality for the norm of a single monic factor of a monic polynomial. The best constants in both inequalities are obtained by potential theoretic methods. We also consider applications of the general results to the cases of a disk and a segment.
Citation
Pritsker, I.E. (2001). Norms of products and factors polynomials. https://doi.org/10.48550/arxiv.math/0101164