On the simultaneous approximation of a Hilbert transform and its derivatives on the real semiaxis

DOI10.1016/j.apnum.2016.12.002zbMath1357.65309OpenAlexW2560730673MaRDI QIDQ509430

Donatella Occorsio, Maria Carmela De Bonis

Publication date: 9 February 2017

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2016.12.002

zbMATH Keywords

stabilityconvergencenumerical exampleorthogonal polynomialsLagrange interpolationapproximation by polynomialsHadamard finite part integralsweighted Hilbert transform

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10)

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Cites Work

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• A method to evaluate the Hilbert transform on (\(0, +\infty \))
• Some quadrature formulae with nonstandard weights
• Numerical integration schemes for Petrov-Galerkin infinite BEM
• \(L^p\)-convergence of Lagrange interpolation on the semiaxis
• Extended Lagrange interpolation in weighted uniform norm
• Definitions, properties and applications of finite-part integrals
• On interpolation of L//p[a,b and weighted Sobolev spaces]
• Numerical evaluation of hypersingular integrals
• Approximation of the Hilbert transform on the real semiaxis using Laguerre zeros
• On the numerical solution of singular integro-differential equations
• Some numerical methods for second-kind Fredholm integral equations on the real semiaxis
• On the Uniform Convergence of Gaussian Quadrature Rules for Cauchy Principal Value Integrals and Their Derivatives
• Truncated Quadrature Rules Over $(0,\infty)$ and Nyström-Type Methods
• A direct approach for boundary integral equations with high-order singularities
• Lagrange interpolation at Laguerre zeros in some weighted uniform spaces

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