Inequalities for products of polynomials I

• Autores: Igor E. Pritsker, Stephan Ruscheweyh
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 104, Nº 1, 2009, págs. 147-160
• Idioma: inglés
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• Resumen

  • 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.