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

  • B. I. Golubov Moscow Inst. Phys. and Technol. (State Univ.), Russia
  • S. S. Volosivets Saratov State Univ., Russia

Abstract

For functions fL1(R+) with cosine (sine) Fourier transforms ˆfc(ˆfs) in L1(R), we give necessary and sufficient conditions in terms of ˆfc(ˆfs) for f to belong to generalized Lipschitz classes Hω,m and hω,m. Conditions for the uniform convergence of the Fourier integral and for the existence of the Schwartz derivative are also obtained.
Published
25.05.2012
How to Cite
Golubov, B. I., and S. S. Volosivets. “Fourier Cosine and Sine Transforms and Generalized Lipschitz Classes in Uniform Metric”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 5, May 2012, pp. 616-27, https://umj.imath.kiev.ua/index.php/umj/article/view/2602.
Section
Research articles