论文标题
一般傅立叶系列收敛的一些问题
Some problems of convergence of general Fourier series
论文作者
论文摘要
S. Banach \ cite {Banach}证明了功能的良好差异特性不能保证A.E.相对于一般的正交系统（ONS），此功能的傅立叶序列的收敛。另一方面，众所周知，A.E.有足够的条件正常序列的收敛是由Menshov-Rademacher定理给出的。 该论文处理了正数$（d_n）$的顺序，以使函数的傅立叶系数$（c_n（f））$乘以这些数字有界变化的函数，一个人获得了A.E. $ \ sum_ {n = 1}^{\ infty} d_n c_n（f）φ_n（x）。$ convertent系列的串联系列。
S. Banach \cite{Banach} proved that good differential properties of function do not guarantee the a.e. convergence of the Fourier series of this function with respect to general orthonormal systems (ONS). On the other hand it is very well known that a sufficient condition for the a.e. convergence of an orthonormal series is given by the Menshov-Rademacher Theorem. The paper deals with sequence of positive numbers $(d_n)$ such that multiplying the Fourier coefficients $(C_n(f))$ of functions with bounded variation by these numbers one obtains a.e. convergent series of the form $\sum_{n=1}^{\infty}d_n C_n(f) φ_n (x).$ It is established that the resulting conditions are best possible.
