On approximations for functions in the space of uniformly convergent Fourier series

DOI10.1016/j.jat.2019.105307zbMath1431.42003OpenAlexW2981572916MaRDI QIDQ2007611

Volker Pohl, Holger Boche

Publication date: 22 November 2019

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2019.105307

zbMATH Keywords

samplingapproximationFourier seriesuniform recoveryTuring computable

Mathematics Subject Classification ID

Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Sampling theory in information and communication theory (94A20) Classical models of computation (Turing machines, etc.) (68Q04)

Cites Work

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• \(\ell _{1}\)-summability of higher-dimensional Fourier series
• L\({}^ 1\)-convergence of Fourier series with O-regularly varying quasimonotonic coefficients
• Advanced topics in system and signal theory. A mathematical approach
• New Banach space properties of the disc algebra and \(H^{\infty}\)
• Schauder bases in Banach spaces of continuous functions
• Uniform convergence of Fourier--Jacobi series.
• Pointwise convergence of cone-like restricted two-dimensional \((C,1)\) means of trigonometric Fourier series
• On convergence and growth of partial sums of Fourier series
• Turing's Legacy
• On uniformly bounded bases in spaces of holomorphic functions
• Modern Fourier Analysis
• On the Calculation of the Hilbert Transform From Interpolated Data
• On Bases in the Disc Algebra
• On Computable Numbers, with an Application to the Entscheidungsproblem. A Correction
• Systems of Logic Based on Ordinals^†
• Pointwise convergence of Fourier series