Fourier cosine and sine transforms and generalized Lipschitz classes in uniform metric
Abstract
For functions f∈L1(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.
Issue
Section
Research articles