\(L^1\) convergence of Fourier transforms revisited

DOI10.1007/s00025-022-01782-6zbMath1504.42013OpenAlexW4308573798MaRDI QIDQ2095499

Elijah Liflyand

Publication date: 17 November 2022

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

Full work available at URL: https://doi.org/10.1007/s00025-022-01782-6

zbMATH Keywords

Fourier transformintegrabilitybounded variationtrigonometric series\(L^1\) convergence

Mathematics Subject Classification ID

Function spaces arising in harmonic analysis (42B35) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Cites Work

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• Fourier transforms on an amalgam type space
• The convolution algebra \(H^{1}(R)\)
• On asymptotics of Fourier transform for functions of certain classes
• The Banach algebra \(A^*\) and its properties
• Functions of bounded variation and their Fourier transforms
• \(L^1\) convergence of Fourier transforms
• Wiener algebras and trigonometric series in a coordinated fashion
• On conditions of the average convergence (upper boundedness) of trigonometric series
• On the spectral synthesis of bounded functions
• Weighted Hankel transform and its applications to Fourier transform
• Harmonic Analysis on the Real Line
• Decay of the Fourier Transform
• Linear Functionals Connected with Strong Cesàro Summability
• A class of trigonometric series

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