Convergence and divergence of higher-order Hermite or Hermite-Fejér interpolation polynomials with exponential-type weights
type: Item
instance of: scholarly article
title: Convergence and divergence of higher-order Hermite or Hermite-Fejér interpolation polynomials with exponential-type weights
zbMATH Open document ID: 1241.41002
DOI: 10.5402/2012/904169
author: Hee Sun Jung
author: Gou Nakamura
author: Ryozi Sakai
author: Noriaki Suzuki
published in: ISRN Mathematical Analysis
publication date: 2012-06-26T00:00:00Z
review text: Summary: Let \(\mathbb R = (-\infty, \infty)\), and let \(w_\rho(x) = |x|^\rho e^{-Q(x)}\), where \(\rho > -1/2\) and \(Q \in C^1(\mathbb R) : \mathbb R \rightarrow \mathbb R^+ = [0, \infty)\) is an even function. Then we can construct the orthonormal polynomials \(p_n(w^2_\rho; x)\) of degree \(n\) for \(w^2_\rho(x)\). In this paper for an even integer \(v \geq 2\) we investigate the convergence theorems with respect to the higher-order Hermite and Hermite-Fejér interpolation polynomials and related approximation process based at the zeros \(\{x_{k,n,\rho}\}^n_{k=1}\) of \(p_n(w^2_{\rho}; x)\). Moreover, for an odd integer \(v \geq 1\), we give a certain divergence theorem with respect to the higher-order Hermite-Fejér interpolation polynomials based at the zeros \(\{x_{k,n,\rho}\}^n_{k=1}\) of \(p_n(w^2_\rho; x)\).
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 42C05
zbMATH DE Number: 6049793
Wikidata QID: Q58693129
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/904169
OpenAlex ID: W2075161809
cites work: Pointwise convergence of Hermite-Fejér interpolation of higher order for Freud weights
cites work: Convergence of the derivatives of Hermite-Fejér interpolation polynomials of higher order based at the zeros of Freud polynomials
cites work: Hermite and Hermite-Fejér interpolation and associated product integration rules on the real line: The \(L_ \infty\) theory
cites work: Uniform or mean convergence of Hermite-Fejér interpolation of higher order for Freud weights
cites work: Orthonormal polynomials with generalized Freud-type weights.
cites work: Orthonormal polynomials for generalized Freud-type weights and higher-order Hermite-Fejér interpolation polynomials
cites work: Q4670241
cites work: Q3367454
cites work: Orthogonal polynomials for exponential weights
cites work: SPECIFIC EXAMPLES OF EXPONENTIAL WEIGHTS
cites work: The Markov-Bernstein inequality and Hermite-Fejér interpolation for exponential-type weights
cites work: Q4026700
cites work: The degree of approximation of differentiable functions by Hermite interpolation polynomials
cites work: Certain unbounded Hermite-Fejér interpolatory polynomial operators
cites work: Q4291323
cites work: Q4291351
cites work: Derivatives of orthonormal polynomials and coefficients of Hermite-Fejér interpolation polynomials with exponential-type weights
cites work: Orthonormal polynomials with exponential-type weights
cites work: Derivatives of integrating functions for orthonormal polynomials with exponential-type weights
cites work: Q3406470
cites work: Q3950972
description: scientific article; zbMATH DE number 6049793