REMEZ-TYPE INEQUALITIES AND THEIR APPLICATIONS Academic Article

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 Mntz 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.

authors

• Erdelyi, Tamas

published proceedings

• JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

author list (cited authors)

• ERDELYI, T.

citation count

• 25

complete list of authors

• ERDELYI, T

publication date

• January 1993

publisher

• Elsevier  Publisher

published in

• Journal of Computational and Applied Mathematics  Journal

keywords

• Bernstein-type, Markov-type, Nikolskii-type And Remez-type Inequalities
• Exponentials Of Logarithmic Potentials
• Generalized Jacobi Weight Functions
• Generalized Polynomials
• Muntz Polynomials

Digital Object Identifier (DOI)

• 10.1016/0377-0427(93)90003-T

start page

• 167

end page

• 209

volume

• 47

issue

• 2

URL

• http%3A%2F%2Fdx.doi.org%2F10.1016%2F0377-0427%2893%2990003-t

user-defined tag

• 10 Reduced Inequalities