某些三角级数的超越性

本文在仅与系数有关的一般条件下证明了某些代数系数三角级数及其导数在代数点上值的超越性.定理的证明基于一个关于数域上的线性无关性的判别法则.     

某些三角级数值的代数无关性

在本文中,笔者研究了复域上的代数系数三角级数及其导数在代数点上值的代数无关性.     

关于二重三角级数的有关讨论

文 [1 ]对形如 ∑∞n =0 ∑∞m =0amncosmxcosny等二重三角级数的和函数进行了研究 ,并证明了其范数‖f(x ,y)‖ p =∫π-π∫π-π｜f(x ,y) ｜p1 dx p2 /p1 dy1/p2 <∞所满足的几个不等式 .本文在此基础上对有关问题作了讨论并得到进一步的结果     

二重三角级数和函数的范数研究

对形如 ∞n=0 ∞m=0amncosmxcosny等二重三角级数的和函数进行了研究 ,并证明了其范数‖f(x ,y)‖ p =∫π-π∫π-π｜f(x ,y) ｜p1dxp2 /p1dy1 /p2 <∞所满足的几个不等式 .     

某些无穷乘积的超越性

本文给出某些用无穷乘积表示的函数在代数点和超越点上的值的超越性．     

数域上的线性无关性

本文给出一组复数在数域上线性无关的一个判别法则及它对于超越数论的一个应用．     

数域上的线性无关性(Ⅱ)

本文给出了文[1](见本刊中文版, 1997,40(5):713-716)中建立的复数在数域上线性无关的判别法则的一个等价形式,并将它应用于某些幂级数和三角级数的超越性研究.     

Trigonometric series with general monotone coefficients

We study trigonometric series with general monotone coefficients. Convergence results in the different metrics are obtained. Also, we prove a Hardy-type result on the behavior of the series near the origin.     

三角级数求和的两种方法

借助实例介绍如何利用傅立叶级数和复变函数的幂级数这两种工具解决有关三角级数的求和问题.     

一类三角级数的收敛性

利用Euler公式求三角级∞∑m=1 sinmx/n与∞∑m=1 cosmx/m的和函数并讨论其一致收敛性.     

Series solutions of some anharmonic motion equations

Consider the class of nonlinear oscillators of the form

(1)     

某些级数的无理性

本文证明了某些与二阶线性递推数列有关的无穷级数的和的无理性．特别，推广了某些与Ｆｉｂｏｎａｃｃｉ和Ｌｕｃａｓ数列有关的无理性结果     

一类三角级数的最佳逼近度

本文在复值连续函数空间中给出一类具有O-正则变化拟单调系数之三角级数的最佳逼近度的一个完备结果.特别是第3节的定理3.2,即使在实连续函数空间中亦是一个新的结论,而且也是Xie与Zhou[6]的定理2在一个方向上的本质推广.最后,在第4节给出一个应用.     

三角级数属于Ba空间的充分必要条件

该文给出了正弦级数和余弦级数在系数满足NBV条件时属于Ba空间的充分必要条件,所得结论 为Ba空间中的首个此类结果,同时也是对L_p空间中已有结论的本质性推广.     

Trigonometric identities in *-algebras

We deal with two systems of trigonometric equations where unknown functions are defined on a group and take values in a (not-necessarily commutative) complex algebra with involution. Our purpose is to give some extension of sine and cosine functions from the scalar to the vector case.     

A Condition for Convergence in Mean of Trigonometric Series

We construct an example of a trigonometric series showing that a certain condition closely related to convergence in mean of trigonometric series cannot be sharpened.     

一类三角级数一致收敛性的一个注记

本文给出对Telyakovskii关于具有微少改变系数的三角级数一致收敛性的结果的本质推广．     

Uniform Convergence of Trigonometric Series with Rarely Changing Coefficients

We consider the series and whose coefficients satisfy the condition for , where the sequence can be expressed as the union of a finite number of lacunary sequences. The following results are obtained. If as , then the series is uniformly convergent. If for all , then the sequence of partial sums of this series is uniformly bounded. If the series is convergent for and as , then this series is uniformly convergent. If the sequence of partial sums of the series for is bounded and for all , then the sequence of partial sums of this series is uniformly bounded. In these assertions, conditions on the rates of decrease of the coefficients of the series are also necessary if the sequence is lacunary. In the general case, they are not necessary.     

On Pointwise Divergence of Trigonometric Series of General Type

Mathematical Notes -