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Ukrainian Mathematical Journal

, Volume 64, Issue 5, pp 693–710 | Cite as

Fourier cosine and sine transforms and generalized Lipschitz classes in the uniform metric

  • B. I. Golubov
  • S. S. Volosivets
Article
  • 72 Downloads

For functions fL 1 (ℝ+) with cosine (sine) Fourier transforms \( {{\hat{f}}_c} \) \( \left( {{{\hat{f}}_s}} \right) \) in L 1 (ℝ), we give necessary and sufficient conditions in terms of \( {{\hat{f}}_c} \) \( \left( {{{\hat{f}}_s}} \right) \) for f to belong to generalized Lipschitz classes H ω,m and h ω,m Conditions for the uniform convergence of the Fourier integral and for the existence of the Schwartz derivative are also obtained.

Keywords

Fourier Series Inversion Formula Trigonometric Series Similar Assertion FOURIER Cosine 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • B. I. Golubov
    • 1
  • S. S. Volosivets
    • 2
  1. 1.Moscow Institute of Physics and Technology (State University)MoscowRussia
  2. 2.Saratov State UniversitySaratovRussia

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