Orthonormal polynomials for generalized Freud-type weights and higher-order Hermite-Fejér interpolation polynomials

DOI10.1016/j.jat.2004.01.006zbMath1053.42026OpenAlexW2013422031MaRDI QIDQ1826865

Ryozi Sakai, Tatsuro Kasuga

Publication date: 6 August 2004

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2004.01.006

zbMATH Keywords

orthonormal polynomialsMarkov inequalitiesgeneralized Freud-type weightshigher order Hermite-Fejér interpolation

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) Interpolation in approximation theory (41A05)

Related Items (7)

Some Fourier-type operators for functions on unbounded intervals ⋮ Convergence and divergence of higher-order Hermite or Hermite-Fejér interpolation polynomials with exponential-type weights ⋮ On the Hermite-Fejér interpolation based at the zeros of generalized Freud polynomials ⋮ Some properties of orthogonal polynomials for Laguerre-type weights ⋮ A Lagrange-type projector on the real line ⋮ Derivatives of orthonormal polynomials and coefficients of Hermite-Fejér interpolation polynomials with exponential-type weights ⋮ Hermite-Fejér and Grünwald interpolation at generalized Laguerre zeros

Cites Work

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• Estimates of Christoffel functions of generalized Freud-type weights
• Weights on the real line that admit good relative polynomial approximation, with applications
• Canonical products and the weights \(\exp (-| x| ^{\alpha})\), \(\alpha >1\), with applications
• Christoffel functions, orthogonal polynomials, and Nevai's conjecture for Freud weights
• The weighted \(L_ p\)-norms of orthonormal polynomials for Freud weights
• \(L_ p\) Markov-Bernstein inequalities for Freud weights
• Pointwise convergence of Hermite-Fejér interpolation of higher order for Freud weights
• Orthonormal polynomials with generalized Freud-type weights.
• Convergence of the derivatives of Hermite-Fejér interpolation polynomials of higher order based at the zeros of Freud polynomials
• $L_\infty $ Markov and Bernstein Inequalities for Freud Weights

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