Mean approximation of functions on the real axis by algebraic polynomials with Chebyshev-Hermite weight and widths of function classes

DOI10.1134/S0001434614050046zbMath1314.41010MaRDI QIDQ2342019

Yanyan Li

Publication date: 8 May 2015

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

modulus of continuityHölder's inequalityJackson-Stechkin type inequalitiesFourier-Hermite seriesChebyshev-Hermite weightmean approximation by algebraic polynomialswidth of a function class

Mathematics Subject Classification ID

Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Approximation by polynomials (41A10)

Related Items (11)

Approximation by classical orthogonal polynomials with weight in spaces \(L_{2, \gamma }(a,b)\) and widths of some functional classes ⋮ On the best approximation in the mean of functions of a complex variable by Fourier series in the Bergman space ⋮ On estimates of diameter values of classes of functions in the weight space \(L_{2, \gamma } ( \mathbb{R}^2)\), \(\gamma = \exp(-x^2 - y^2)\) ⋮ On the best polynomial approximation in Hardy space ⋮ On the estimates of the values of various widths of classes of functions of two variables in the weight space \(L_{2, \gamma } ( \mathbb{R}^2)\), \(\gamma = \exp ( - x^2 - y^2)\) ⋮ K-FUNCTIONALS AND EXACT VALUES OF n-WIDTHS IN THE BERGMAN SPACE ⋮ Upper bounds for the approximation of certain classes of functions of a complex variable by Fourier series in the space \(L_2\) and \(n\)-widths ⋮ Approximation of Bivariate Functions by Fourier-Tchebychev ``Circular Sums in $L_{2,\rho}$ ⋮ On the estimates of widths of the classes of functions defined by the generalized moduli of continuity and majorants in the weighted space \(L_{2,x}(0, 1)\) ⋮ \(K\)-functionals and extreme problems of the approximation theory for classes of analytic functions in a circle. I ⋮ Widths of the classes of functions in the weight space \(L_{2 , \gamma } (\mathbb{R})\), \(\gamma = \mathrm{exp} ( - X^2)\)

Cites Work

• Jackson-type inequalities and widths of function classes in \(L_{2}\)
• A sharp inequality of Jackson-Stechkin type in \(L_{2}\) and the widths of functional classes
• Weighted polynomial approximation
• K functionals and best polynomial approximation in weighted \(L^ p(R)\)
• Polynomial approximation with Chebyshev-Hermite weight on the real axis
• \(K\)-functionals and exact values of \(n\)-widths of some classes in \(L_2\)
• On \(K\)-functionals and exact values of \(n\)-widths of some classes in the spaces \(C(2\pi)\) and \(L_1(2\pi)\)
• Jackson inequalities on sphere in \(L_ 2\)
• An exact Jackson-Stechkin inequality for $ L^2$-approximation on the interval with the Jacobi weight and on projective spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Mean approximation of functions on the real axis by algebraic polynomials with Chebyshev-Hermite weight and widths of function classes