Norms of products and factors polynomials

Details Norms of products and factors polynomials Norms of products and factors polynomials

2001-01-19

arxiv.org/abs/math/0101164v1

Mathematics

Complex Variables

17 pages, 2 figures, Millennial Conference on Number Theory (Urbana, Illinois)

Scientific paper

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.

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