Norms of Products and Factors Polynomials
نویسنده
چکیده
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.
منابع مشابه
Norms of Products and Factors of Polynomials
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 rela...
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