有理Fourier级数在变差条件下的收敛性研究

On convergence of rational Fourier series of functions of bounded variations

本文把Fourier级数的一些经典结论推广到有理Fourier级数的情况下.首先给出了有理Fourier级数和共轭有理Fourier级数在有界变差条件下的收敛速度估计.利用此结论,得到了类似于Fourier级数的Dirichlet-Jordan定理和W.H.Young定理.最后,证明了这两个定理在调和有界变差条件下也成立.

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.