REMEZ-TYPE INEQUALITIES AND THEIR APPLICATIONS

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:47

Article

关键词: BERNSTEIN-TYPE, MARKOV-TYPE, NIKOLSKII-TYPE AND REMEZ-TYPE INEQUALITIES;    GENERALIZED POLYNOMIALS;    EXPONENTIALS OF LOGARITHMIC POTENTIALS;    MUNTZ POLYNOMIALS;    GENERALIZED JACOBI WEIGHT FUNCTIONS;   

DOI  :  10.1016/0377-0427(93)90003-T

来源: Elsevier

【 摘 要 】

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 Absolute value of 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 Muntz 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.

【 授权许可】

Free