Abstract
The author’s recent attempt to generalize the problem of \(L^1\) convergence of trigonometric series to the non-periodic case is finalized here. It can now be said that any known condition which guarantees integrability of the Fourier transform of a function of bounded variation also leads to the \(L^1\) convergence of its partial integrals provided that a universal necessary and sufficient condition is added.
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Liflyand, E. \(L^1\) Convergence of Fourier Transforms Revisited. Results Math 78, 1 (2023). https://doi.org/10.1007/s00025-022-01782-6
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DOI: https://doi.org/10.1007/s00025-022-01782-6