Lower bounds for derivatives of polynomials and Remez type inequalities Academic Article uri icon

abstract

  • P. Turán [Über die Ableitung von Polynomen, Comositio Math. 7 (1939), 89-95] proved that if all the zeros of a polynomial p lie in the unit interval I = [-1,1], then ∥P′∥L∞(1) ≥ √deg(p)/6 ∥p∥L∞(I) . Our goal is to study the feasibility of limn→∞ ∥Pn∥x/HPn∥y = ∞ for sequences of polynomials (pn}n∈N whose zeros satisfy certain conditions, and to obtain lower bounds for derivatives of (generalized) polynomials and Remez type inequalities for generalized polynomials in various spaces. ©1997 American Mathematical Society.

author list (cited authors)

  • Erdélyi, T., & Nevai, P.

citation count

  • 9

publication date

  • January 1997