A MARKOV-TYPE INEQUALITY FOR THE DERIVATIVES OF CONSTRAINED POLYNOMIALS
Academic Article
Overview
Identity
Additional Document Info
Other
View All
Overview
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.