本文用计算围道积分和使用特征函数渐近式的方法得到函数按二阶Sturm-Liouville 算子特征函数展开前 n 项和与其余弦级数的前项和之差的两个估计,这两个估计分别适用于有界可测函数和有界变差函数的特征展开。这样,我们能从函数的余弦...本文用计算围道积分和使用特征函数渐近式的方法得到函数按二阶Sturm-Liouville 算子特征函数展开前 n 项和与其余弦级数的前项和之差的两个估计,这两个估计分别适用于有界可测函数和有界变差函数的特征展开。这样,我们能从函数的余弦级数的收敛速度估计得到函数的特征函数展开的收敛速度估计。展开更多
We prove that for any p perfect set of positive measure and for it＇s any density point x0 one can construct a measurable function f（x）, bounded on [0,1）, such that each measurable and bounded function, which coinc...We prove that for any p perfect set of positive measure and for it＇s any density point x0 one can construct a measurable function f（x）, bounded on [0,1）, such that each measurable and bounded function, which coincides with f（x） on the set p has diverging Fourier-Walsh series on the point xo.展开更多
文摘We prove that for any p perfect set of positive measure and for it＇s any density point x0 one can construct a measurable function f（x）, bounded on [0,1）, such that each measurable and bounded function, which coincides with f（x） on the set p has diverging Fourier-Walsh series on the point xo.
