"Inequalities Concerning the L<sup>p</sup> Norm of a Polynomial and Its" by Robert B. Gardner and Narendra K. Govil
 

Inequalities Concerning the Lp Norm of a Polynomial and Its Derivative

Document Type

Article

Publication Date

1-1-1993

Description

Let Pn(z) = an ∏nv = 1 (z - zv), an ≠ 0, be a polynomial of degree n. It has been proved that if |zv| ≥ Kv ≥ 1, 1 ≤ v ≤ n, then for p ≥ 1, [formula] where Fp = (2π/∫2π0 |t0 + eiΘ)pdΘ)1/p and t0 = (1 + n/∑nv=1 (1/(Kv - 1))). This result generalizes the well known Lp inequality due to De Bruijn for polynomials not vanishing in |z| < 1. On making p → ∞, it gives the L∞ inequality due to Govil and Labelle which as a special case includes the Erdo(combining double acute accent)s conjecture proved by Lax.

Plum Print visual indicator of research metrics
PlumX Metrics
  • Citations
    • Citation Indexes: 13
  • Usage
    • Abstract Views: 1
  • Captures
    • Readers: 2
see details

Share

COinS