Orthogonal polynomials for exponential weights x2α(1 – x2)2ρe–2Q(x) on [0, 1)

Author:

Liu Rong1

Affiliation:

1. College of Computer and Information Sciences, Fujian Agriculture and Forestry University, Fuzhou, Fujian 350002, P. R. China

Abstract

Abstract Let Wα,ρ = xα(1 – x2)ρeQ(x), where α > – $\begin{array}{} \displaystyle \frac12 \end{array}$ and Q is continuous and increasing on [0, 1), with limit ∞ at 1. This paper deals with orthogonal polynomials for the weights $\begin{array}{} \displaystyle W^2_{\alpha, \rho} \end{array}$ and gives bounds on orthogonal polynomials, zeros, Christoffel functions and Markov inequalities. In addition, estimates of fundamental polynomials of Lagrange interpolation at the zeros of the orthogonal polynomial and restricted range inequalities are obtained.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference24 articles.

1. Polynomial inequalities and embedding theorems with exponential weights in (−1, 1);Acta Math. Hungar.,2012

2. Lagrange interpolation with exponential weights on (−1, 1);J. Approx. Theory,2013

3. The zeros of orthogonal for Jacobi-exponential weights;Abstr. Appl. Anal.,2012

4. Lagrange interpolation at Pollaczek-Laguerre zeros on the real semiaxis;J. Approx. Theory,2019

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