A MARKOV-TYPE INEQUALITY FOR THE DERIVATIVES OF CONSTRAINED POLYNOMIALS Academic Article uri icon

abstract

  • Markov's inequality asserts that max -1x1|p(x)|n2 max -1x1|p(x)| (1) for every polynomial of degree at most n. The magnitude of sup pS max-1x1|p(x)| max-1x1|p(x)| (2) was examined by several authors for certain subclasses S of n. In this paper we introduce S = Snm(r) (0 m n, 0 < r 1), the set of those polynomials from n which have all but at most m zeros outside the circle with center 0 and radius r, and establish the exact order of the above expression up to a multiplicative constant depending only on m. 1990.

published proceedings

  • JOURNAL OF APPROXIMATION THEORY

author list (cited authors)

  • ERDELYI, T.

citation count

  • 1

complete list of authors

  • Erdélyi, Tamás

publication date

  • December 1990