L1 Convergence of Fourier Transforms Revisited

E. Liflyand

Research output: Contribution to journalArticlepeer-review


The author’s recent attempt to generalize the problem of L1 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 L1 convergence of its partial integrals provided that a universal necessary and sufficient condition is added.

Original languageEnglish
Article number1
JournalResults in Mathematics
Issue number1
StatePublished - Feb 2023

Bibliographical note

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.


  • Fourier transform
  • L convergence
  • Trigonometric series
  • bounded variation
  • integrability


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