\(L^1\) convergence of Fourier transforms

DOI10.1007/s13324-021-00530-3zbMath1466.42005OpenAlexW3140628411MaRDI QIDQ2031879

Elijah Liflyand

Publication date: 15 June 2021

Published in: Analysis and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13324-021-00530-3

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)

Related Items

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

Cites Work

• On the coefficients of Fourier series convergent in \(L\)
• 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
• On the spectral synthesis of bounded functions
• Decay of the Fourier Transform
• Linear Functionals Connected with Strong Cesàro Summability
• A class of trigonometric series
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