2013•Scientia Sinica MathematicaRequires access
On convergence of rational Fourier series of functions of bounded variations
Tao Qian, LiHui TAN
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Abstract
In this paper, we extended some classical results of Fourier series to rational Fourier series. We give an estimate of convergence rate of the rational Fourier series of functions of bounded variation and an analogous one for the conjugate rational Fourier series. As its applications, we deduce the Dirichlet-Jordan's theorem and W. H. Young's theorem for rational Fourier series of functions of bounded variation. Finally, we extend these two theorems to harmonic bounded variation.