On Fourier Re-Expansions

Elijah Liflyand

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


An old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series is extended to the non-periodic case (Fourier transforms). Necessary and sufficient conditions are given as relations between the Fourier transforms and their Hilbert transforms. Sufficient conditions for integrability of the Hilbert transform are obtained.

Original languageEnglish
Pages (from-to)934-946
Number of pages13
JournalJournal of Fourier Analysis and Applications
Issue number5
StatePublished - Oct 2014

Bibliographical note

Publisher Copyright:
© 2014, Springer Science+Business Media New York.


  • Fourier transform
  • Hardy space
  • Hilbert transform
  • Integrability


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