Approximation of continuous on a segment functions with the help of linear combinations of sincs

DOI10.3103/S1066369X16030087zbMath1346.42004OpenAlexW2310968804MaRDI QIDQ292855

A. Yu. Trynin

Publication date: 9 June 2016

Published in: Russian Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3103/s1066369x16030087

zbMATH Keywords

interpolationuniform approximationsinc-approximation

Mathematics Subject Classification ID

Trigonometric approximation (42A10)

Related Items (11)

Lagrange-Sturm-Liouville processes ⋮ On the convergence of generalizations of the sinc approximations on the Privalov–Chanturia class ⋮ Hardy-Littlewood and Pitt's inequalities for Hausdorff operators ⋮ Sufficient condition for convergence of Lagrange-Sturm-Liouville processes in terms of one-sided modulus of continuity ⋮ Necessary and Sufficient Conditions for the Uniform on a Segment Sinc-approximations Functions of Bounded Variation ⋮ Error estimate for uniform approximation by Lagrange-Sturm-Liouville processes ⋮ The Principle of Localization at the Class of Functions Integrable in the Riemann for the Processes of Lagrange –Sturm – Liouville ⋮ Uniform convergence of Lagrange - Sturm - Liouville processes on one functional class ⋮ On the uniform approximation of functions of bounded variation by Lagrange interpolation polynomials with a matrix of Jacobi nodes ⋮ Sufficient conditions for convergence of generalized sinc-approximations on segment ⋮ Convergence of the Lagrange-Sturm-Liouville Processes for Continuous Functions of Bounded Variation

Uses Software

• MuST

Cites Work

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• Uniform convergence of hyperbolic partial sums of multiple Fourier series.
• The divergence of Lagrange interpolation processes in eigenfunctions of the Sturm-Liouville problem
• A criterion for the uniform convergence of sinc-approximations on a segment
• Absence of stability of interpolation with respect to eigenfunctions of the Sturm-Liouville problem
• Spherical jump of a function and the Bochner-Riesz means of conjugate multiple Fourier series and Fourier integrals
• Orthogonal polynomial Schauder bases in $ C \lbrack -1,1 \rbrack $ with optimal growth of degrees
• On a class of summability methods for multiple Fourier series
• On divergence of sinc-approximations everywhere on $(0,\pi)$
• MuST: The Multilevel Sinc Transform
• On operators of interpolation with respect to solutions of a Cauchy problem and Lagrange-Jacobi polynomials
• Basic wavelet theory
• A generalization of the Whittaker-Kotel'nikov-Shannon sampling theorem for continuous functions on a closed interval
• Tests for pointwise and uniform convergence of sinc approximations of continuous functions on a closed interval
• Absolute convergence of multiple Fourier series

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