加权Hilbert型空间中超齐次核离散算子的最佳搭配参数及范数计算  

Optimal Matching Parameters of Discrete Operator with Super-homogeneous Kernel in Weighted Hilbert-type Space and Norm Calculation

作　　者：张丽娟 洪勇 ZHANG Lijuan;HONY Yong(College of Data Science,Guangzhou Huashang College,Guangzhou 511300,China;College of Statistics and Mathematics,Guangdong University of Finance and Economics,Guangzhou 510320,China)

机构地区：[1]广州华商学院数据科学学院,广东广州511300 [2]广东财经大学统计与数学学院,广东广州510320

出　　处：《应用数学》2024年第2期327-336,共10页Mathematica Applicata

基　　金：广东省基础与应用基础研究基金(2022A1515012429);广州华商学院导师制项目(2023HSDS04)。

摘　　要：引入超齐次核概念,利用权系数方法,讨论具有超齐次核离散算子在加权Hilbert型空间中的有界性及算子范数,得到该类算子最佳搭配参数的充分必要条件和算子范数的计算公式,统一了齐次核,广义齐次核及若干非齐次核情形的相关结果.The concept of super-homogeneous kernel is introduced,and the boundedness of discrete operators with super-homogeneous kernel in weighted Hilbert-type space and operator norm are discussed by the method of weight coefficient,and sufficient necessary conditions for the best matching parameters of this class of operators and the formulas for the operator norm are obtained,unifying the relevant results for the case of the homogeneous kernel,the generalized homogeneous kernel and several non-homogeneous kernels.

关 键 词：超齐次核 Hilbert型离散不等式 离散算子 加权Hilbert空间 最佳搭配参数 

分 类 号：O178[理学—数学]