Inequalities for products of polynomials I

Authors

  • I.E. Pritsker
  • S. Ruscheweyh

DOI:

https://doi.org/10.7146/math.scand.a-15091

Abstract

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.

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Published

2009-03-01

How to Cite

Pritsker, I., & Ruscheweyh, S. (2009). Inequalities for products of polynomials I. MATHEMATICA SCANDINAVICA, 104(1), 147–160. https://doi.org/10.7146/math.scand.a-15091

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Section

Articles