| 一类非齐次核的Hilbert型级数算子最佳搭配参数的充要条件 |
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| 引用本文： | 洪勇,陈强. 一类非齐次核的Hilbert型级数算子最佳搭配参数的充要条件[J]. 数学的实践与认识, 2022, 0(1): 216-222 |
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| 作者姓名： | 洪勇 陈强 |
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| 作者单位： | 1.广州华商学院应用数学系;2.广东第二师范学院计算机科学系 |
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| 基金项目： | 国家自然科学基金(61772140)。 |
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| 摘 要： | 选择搭配参数a,b,利用权函数方法,可得核为K(m,n)的级数算子T的不等式:||T((a))||p,β(a,b) ≤ M(a,b)||(a)||p,α(a,b),(a) ={am}一般地,M(a,b)并不是T:lap(a,b)→lβp(a,b)的算子范数,针对非齐次核K(m,n)=G(mλ1/nλ2)(λ1λ2＞0)...
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| 关 键 词： | Hilbert型级数算子 Hilbert型级数不等式 非齐次核 算子范数 最佳搭配参数 |
The Necessary and Sufficient Conditions for Optimal Matching Parameters of Hilbert-Type Series Operator with a Class of Non-Homogeneous Kernel |
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| HONG Yong,CHEN Qiang. The Necessary and Sufficient Conditions for Optimal Matching Parameters of Hilbert-Type Series Operator with a Class of Non-Homogeneous Kernel[J]. Mathematics in Practice and Theory, 2022, 0(1): 216-222 |
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| Authors: | HONG Yong CHEN Qiang |
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| Affiliation: | (Department of Applied Mathematics,Guangzhou Huashang College,Guangzhou 511300,China;Department of Computer Science,Guangdong University of Education,Guangzhou 510303,China) |
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| Abstract: | By choosing the matching parameters a and b,using the weight function method,the inequality of series operator T with kernel K(m,n):‖T(a)‖p,β(a,B)≤M(a,b)‖a‖p,α(a,b)can be obtained.In general M(a,b)is not the norm of operator T:lpα(a,b)→lpβ(a,b).using the weight function method the paper discusses the necessary and sufficient conditions of the best matching parameters for operator T with non-homogeneous kernel K(m,n)=G(mλ1/nλ2)(λ1λ2>0),and obtaied the norm formula of operator T when a and b are the best matching parameters. |
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| Keywords: | Hilbert-type series operator Hilbert-type series inequality non-homogeneous kernel operator norm the best matching parameter |
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