离散型Hilbert不等式的推广及应用  

On an Extension of the Discrete Type Hilbert Inequality and Its Application

作　　者：有名辉[1] YOU Minghui(Mathematics Teaching and Research Section,Zhejiang Institute of Mechanical and Electrical Engineering,Hangzhou 310053,Zhejiang,China)

机构地区：[1]浙江机电职业技术学院数学教研室,浙江杭州310053

出　　处：《武汉大学学报（理学版）》2021年第2期179-184,共6页Journal of Wuhan University:Natural Science Edition

基　　金：浙江省教育厅科研项目(Y201737260);浙江机电职业技术学院科教融合项目(A-0271-20-007)。

摘　　要：通过引入两个参数,构造了一个离散的分式型的核函数,并由此建立相应的Hilbert不等式。利用余切函数的部分分式展开,证明了所构建的不等式的常数因子可用余切函数表示,且常数因子是最佳的。通过对参数赋值,得到了一些有趣的特殊结果。By introducing two parameters, a discrete kernel function of fraction type is constructed, and the corresponding Hilbert inequality is established. By using the partial fraction expansion of the cotangent function, it is proved that the constant factor of the constructed inequality can be expressed by cotangent function, and the constant factor is optimal. Finally, by specifying the values of parameters, some interesting special results are obtained.

关 键 词：HILBERT不等式 离散型 部分分式展开 余切函数 

分 类 号：O174.1[理学—数学]