Weighted polynomial inequalities

1986 ◽  
Vol 2 (1) ◽  
pp. 113-127 ◽  
Author(s):  
Paul Nevai ◽  
Vilmos Totik
Keyword(s):  
Polynomial Inequalities ◽  
Weighted Polynomial Inequalities

Weighted Polynomial Inequalities with Doubling and A ∞ Weights

2000 ◽  
Vol 16 (1) ◽  
pp. 37-71 ◽  
Author(s):  
Giuseppe Mastroianni ◽  
Vilmos Totik
Keyword(s):  
Polynomial Inequalities ◽  
Weighted Polynomial Inequalities

A SURVEY OF POLYNOMIAL APPROXIMATION ON THE SPHERE

2009 ◽  
Vol 07 (06) ◽  
pp. 749-771 ◽  
Author(s):  
FENG DAI ◽  
KUNYANG WANG
Keyword(s):  
Polynomial Approximation ◽  
Moduli Of Smoothness ◽  
Spherical Approximation ◽  
Jackson Inequality ◽  
Cesàro Means ◽  
Bernstein Type ◽  
Cubature Formulas ◽  
Polynomial Inequalities ◽  
Spherical Polynomials ◽  
Weighted Polynomial Inequalities

The main purpose of this paper is to survey some of the work on spherical approximation done by the BNU group under the direction of Professor Sun. The equiconvergent operators of Cesàro means, and their interesting applications are described. The Jackson inequality for spherical polynomials and some moduli of smoothness on the sphere are investigated. The equivalence between moduli of smoothness and K-functionals is also discussed. We also describe several weighted polynomial inequalities on the sphere, including the Remez-type and the Nikolskii-type inequalities, the Marcinkiewicz–Zygmund inequality, the Bernstein-type and the Schur-type inequalities. Positive cubature formulas on the sphere, and their relation to the Marcinkiewicz–Zygmund inequality are also discussed. A survey on recent results on asymptotic orders of the n-widths of Sobolev's classes on the sphere is also given.

scholarly journals Markov type polynomial inequality for some generalized Hermite weight

2011 ◽  
Vol 49 (1) ◽  
pp. 111-118
Author(s):  
Branislav Ftorek ◽  
Mariana Marˇcokov´A
Keyword(s):  
Weight Function ◽  
Hermite Polynomials ◽  
Polynomial Inequality ◽  
Markov Type ◽  
Polynomial Inequalities ◽  
Weighted Polynomial Inequalities ◽  
Special Case

ABSTRACT In this paper we study some weighted polynomial inequalities of Markov type in L2-norm. We use the properties of the system of generalized Hermite polynomials . The polynomials H(α)n (x) are orthogonal in ℝ = (−∞,∞) with respect to the weight function . The classical Hermite polynomials Hn(x) present the special case for α = 0.

scholarly journals Polynomial inequalities on the Hamming cube

2020 ◽  
Vol 178 (1-2) ◽  
pp. 235-287
Author(s):  
Alexandros Eskenazis ◽  
Paata Ivanisvili
Keyword(s):  
Polynomial Inequalities
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