构建超齐次核有界离散算子的参数条件及算子范数估计

数学物理学报 ›› 2024, Vol. 44 ›› Issue (4): 837-846.

构建超齐次核有界离散算子的参数条件及算子范数估计

洪勇(),赵茜^*()

广州华商学院数据科学学院广州 511300

收稿日期:2023-07-17 修回日期:2024-01-10 出版日期:2024-08-26 发布日期:2024-07-26
通讯作者: *赵茜, E-mail:eunicezhao_777@163.com
作者简介:洪勇, E-mail:hongyonggdcc@yeah.net
基金资助:
广东省基础与应用基础研究基金(2022A1515012429);广州华商学院科研团队项目(2021HSKT03)

Parameter Conditions for Constructing Bounded Discrete Operators with Super-Homogeneous Kernel and Estimation of the Operator Norm

Hong Yong(),Zhao Qian^*()

College of Data Science, Guangzhou Huashang College, Guangzhou 511300

Received:2023-07-17 Revised:2024-01-10 Online:2024-08-26 Published:2024-07-26
Supported by:
Fundamental and Applied Basic Research Program of Guangdong Province(2022A1515012429);Guangzhou Huashang College Research Team Program(2021HSKT03)

摘要/Abstract

摘要：

引入超齐次函数的概念, 首先构建超齐次核的 Hilbert 型离散不等式, 然后利用 Hilbert 型不等式与同核算子的关系, 讨论超齐次核离散算子,得到加权赋范序列空间中超齐次核有界离散算子的构建条件, 解决了算子是否有界的判定方法和算子范数的估计问题.

关键词: 超齐次核, 有界算子, 加权序列空间, 有界算子的判定, Hilbert型离散不等式, 算子范数

Abstract:

Introducing the concept of super-homogeneous function, firstly constructing the Hilbert-type discrete inequality with super-homogeneous kernel, and then discussing discrete operator with super-homogeneous kernel by using the relationship between Hilbert-type inequality and operator with the same kernel, obtained the construction conditions for bounded discrete operators with super-homogeneous kernel in weighted normed sequence spaces, and a method for determining whether an operator is bounded or not and the estimation of operator norm are solved.

Key words: Super-homogeneous function, Bounded discrete operator, Weighted sequence spaces, Determination of bounded operators, Hilbert-type discrete inequality, Operator norm

中图分类号:

O177

洪勇, 赵茜. 构建超齐次核有界离散算子的参数条件及算子范数估计[J]. 数学物理学报, 2024, 44(4): 837-846.

Hong Yong, Zhao Qian. Parameter Conditions for Constructing Bounded Discrete Operators with Super-Homogeneous Kernel and Estimation of the Operator Norm[J]. Acta mathematica scientia,Series A, 2024, 44(4): 837-846.

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