REMEZ-TYPE INEQUALITIES AND THEIR APPLICATIONS

被引：33
作者：
ERDELYI, T
机构：
[1] Department of Mathematics, The Ohio State University, Columbus, OH
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1993年 / 47卷 / 02期
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;
D O I：
10.1016/0377-0427(93)90003-T
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
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.
引用
收藏
页码：167 / 209
页数：43
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