Pointwise and uniform convergence of Fourier extensions

DOI10.1007/s00365-019-09486-xzbMath1444.42003arXiv1811.09527OpenAlexW2991544909WikidataQ126806979 ScholiaQ126806979MaRDI QIDQ784753

Marcus Webb, Daan Huybrechs, Vincent Coppé

Publication date: 3 August 2020

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1811.09527

zbMATH Keywords

Lebesgue functionFourier extensionconstructive approximationLegendre polynomials on a circular arc

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Inequalities in approximation (Bernstein, Jackson, Nikol'ski?-type inequalities) (41A17) General harmonic expansions, frames (42C15) Numerical methods for trigonometric approximation and interpolation (65T40)

Related Items (4)

Insight into the Stability Analysis of the Reaction-Diffusion Equation Interconnected with a Finite-Dimensional System Taking Support on Legendre Orthogonal Basis ⋮ Fast and stable approximation of analytic functions from equispaced samples via polynomial frames ⋮ The Fourier extension method and discrete orthogonal polynomials on an arc of the circle ⋮ A robust spline approach in partially linear additive models

Uses Software

• DLMF
• Chebfun
• ApproxFun
• GitHub

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the numerical stability of Fourier extensions
• Parameter selection and numerical approximation properties of Fourier extensions from fixed data
• The prolate matrix
• A comparison of numerical algorithms for Fourier extension of the first, second, and third kinds
• Approximation error in regularized SVD-based Fourier continuations
• Fourier embedded domain methods: Extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and \(C^{\infty}\)
• Interpolation and approximation by polynomials
• The Riemann--Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
• Bernstein's inequality for algebraic polynomials on circular arcs
• Freud equations for Legendre polynomials on a circular arc and solution of the Grünbaum-Delsarte-Janssen-Vries problem.
• The fast Slepian transform
• Accurate, high-order representation of complex three-dimensional surfaces via Fourier continuation analysis
• On the resolution power of Fourier extensions for oscillatory functions
• A class of orthogonal polynomials
• Fast Algorithms for the Computation of Fourier Extensions of Arbitrary Length
• On the Fourier Extension of Nonperiodic Functions
• A Fast Algorithm for Fourier Continuation
• Extension of Chebfun to Periodic Functions
• On the Periodic Discrete Prolate Spheroidal Sequences
• Prolate Spheroidal Wave Functions, Fourier Analysis, and Uncertainty-V: The Discrete Case
• Function Approximation on Arbitrary Domains Using Fourier Extension Frames
• Computing with Functions on Domains with Arbitrary Shapes
• Frames and Numerical Approximation
• On the convergence rates of Legendre approximation

This page was built for publication: Pointwise and uniform convergence of Fourier extensions