A sharp error estimate for numerical Fourier fransform of band-limited functions based on windowed samples

DOI10.4171/ZAA/1490zbMath1279.41025MaRDI QIDQ380257

Steffen J. Goebbels

Publication date: 13 November 2013

Published in: Zeitschrift für Analysis und ihre Anwendungen (Search for Journal in Brave)

zbMATH Keywords

Fourier transformwindow functionsaliasingresonance principlesharp error bounds

Mathematics Subject Classification ID

Numerical methods for discrete and fast Fourier transforms (65T50) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Rate of convergence, degree of approximation (41A25)

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On sharpness of error bounds for univariate approximation by single hidden layer feedforward neural networks

Cites Work

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• Quantitative condensation of singularities for convolution processes of Fejér-type
• Growth properties of Fourier transforms via moduli of continuity
• Quantitative extensions of the uniform boundedness principle
• Sharp estimates in terms of moduli of smoothness for compound cubature rules
• A unified approach to certain counterexamples in approximation theory in connection with a uniform boundedness principle with rates
• A sharp error estimate for the numerical solution of a Dirichlet problem for the Poisson equation
• On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin-methods
• The sharpness of a pointwise error bound for the Fejér-Hermite interpolation process on sets of positive measure
• On the sharpness of error bounds for the numerical solution of initial boundary value problems by finite difference schemes
• A sharp error bound in terms of an averaged modulus of smoothness for Fourier Lagrange coefficients
• Sampling Theory for not Necessarily Band-Limited Functions: A Historical Overview
• The sharpness of a pointwise error bound in connection with linear finite elements
• On the sharpness of error bounds in connection with finite difference schemes on uniform grids for boundary value problems of ordinary differential equations
• A resonance principle with rates in connection with pointwise estimates for the approximation by interpolation processes

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