Markov-Bernstein-type inequalities for classes of polynomials with restricted zeros Academic Article uri icon


  • We prove that an absolute constant c>0 exists such that {Mathematical expression} for every real algebraic polynomial of degree at most n having at most k zeros in the open unit disk {z∈C:|z|<1}. This inequality, which has been conjectured for at least a decade, improves and generalizes several earlier results. Up to the multiplicative absolute constant c, it is a sharp generalization of both Markov's and Bernstein's inequalities. © 1994 Springer-Verlag New York Inc.

author list (cited authors)

  • Borwein, P., & Erdélyi, T.

citation count

  • 10

publication date

  • September 1994