Conditions for the absolute convergence of Fourier integrals

E. Liflyand, R. Trigub

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

New sufficient conditions for the representation of a function via an absolutely convergent Fourier integral are obtained in the paper. In the main result, this is controlled by the behavior near infinity of both the function and its derivative. This result is extended to any dimension d≥2.

Original languageEnglish
Pages (from-to)438-459
Number of pages22
JournalJournal of Approximation Theory
Volume163
Issue number4
DOIs
StatePublished - Apr 2011

Bibliographical note

Funding Information:
The work of the second author was also supported by the Ukranian Fund for Fundamental Research Ukraine, Project F25. 1/055.

Keywords

  • Fourier integral
  • Fourier multiplier
  • Vitali variation

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