Remez-type inequalities and their applications Academic Article uri icon

abstract

  • The Remez inequality gives a sharp uniform bound on [-1, 1] for real algebraic polynomials p of degree at most n if the Lebesgue measure of the subset of [-1, 1], where |;p|; is at most 1, is known. Remez-type inequalities give bounds for classes of functions on a line segment, on a curve or on a region of the complex plane, given that the modulus of the functions is bounded by 1 on some subset of prescribed measure. This paper offers a survey of the extensive recent research on Remez-type inequalities for polynomials, generalized nonnegative polynomials, exponentials of logarithmic potentials and Müntz polynomials. Remez-type inequalities play a central role in proving other important inequalities for the above classes. The paper illustrates the power of Remez-type inequalities by giving a number of applications. © 1993.

author list (cited authors)

  • Erdélyi, T.

citation count

  • 20

publication date

  • January 1993