A method to evaluate the Hilbert transform on (\(0, +\infty \))

DOI10.1016/j.amc.2010.12.045zbMath1209.65139OpenAlexW2049336460MaRDI QIDQ628936

Donatella Occorsio

Publication date: 8 March 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2010.12.045

zbMATH Keywords

orthogonal polynomialsnumerical examplesHilbert transformLagrange interpolationerror estimateLaguerre polynomialsapproximation by polynomialstruncated Gaussian rules

Mathematics Subject Classification ID

Numerical methods for integral transforms (65R10)

Related Items (6)

Approximation of Hilbert and Hadamard transforms on \((0,+\infty)\) ⋮ A new quadrature scheme based on an extended Lagrange interpolation process ⋮ Numerical computation of hypersingular integrals on the real semiaxis ⋮ On the simultaneous approximation of a Hilbert transform and its derivatives on the real semiaxis ⋮ Limits of calculating the finite Hilbert transform from discrete samples ⋮ Error bounds for a Gauss-type quadrature rule to evaluate hypersingular integrals

Uses Software

• OrthogonalPolynomials

Cites Work

• Extended Lagrange interpolation in weighted uniform norm
• Approximation of the Hilbert transform on the real semiaxis using Laguerre zeros
• Numerical approximation of weakly singular integrals on the half line
• Orthonormal polynomials with generalized Freud-type weights.
• Interlacing properties of the zeros of the orthogonal polynomials and approximation of the Hilbert transform
• Orthogonal polynomials for exponential weights \(x^{2\rho} e^{-2Q(x)}\) on \([0,d)\). II.
• A class of orthogonal polynomials
• Approximation of the Hilbert Transform on the Real Line Using Freud Weights
• A Nyström Method for Solving a Boundary Value Problem on [0, ∞)
• Numerical construction of the generalized Hermite polynomials
• Some numerical methods for second-kind Fredholm integral equations on the real semiaxis
• Half-Range Generalized Hermite Polynomials and the Related Gaussian Quadratures
• Truncated Quadrature Rules Over $(0,\infty)$ and Nyström-Type Methods
• Approximation of the Hilbert Transform on the real line using Hermite zeros
• Lagrange interpolation at Laguerre zeros in some weighted uniform spaces
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