The Fourier transforms of general monotone functions

E. Liflyand, S. Tikhonov

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

Extending the notion of the general monotonicity for sequences to functions, we exploit it to investigate integrability problems for Fourier transforms. The problem of controlling integrability properties of the Fourier transform separately near the origin and near infinity is examined. We then apply the obtained results to the problems of integrability of trigonometric series.

Original languageEnglish
Title of host publicationAnalysis and Mathematical Physics
EditorsBjörn Gustafsson, Alexander Vasilev
PublisherSpringer International Publishing
Pages377-395
Number of pages19
ISBN (Print)9783764399054
DOIs
StatePublished - 2009
EventInternational Conference on New trends in harmonic and complex analysis, 2007 - Trondheim, Norway
Duration: 7 May 200712 May 2007

Publication series

NameTrends in Mathematics
Volume46
ISSN (Print)2297-0215
ISSN (Electronic)2297-024X

Conference

ConferenceInternational Conference on New trends in harmonic and complex analysis, 2007
Country/TerritoryNorway
CityTrondheim
Period7/05/0712/05/07

Bibliographical note

Publisher Copyright:
© 2009 Birkhäuser Verlag Basel/Switzerland.

Keywords

  • Bounded variation
  • Fourier transform
  • Monotone/general monotone functions
  • Trigonometric series

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