| Hilbert空间上依范连续的α-次预解算子族 |
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| 引用本文： | 刘茹,李淼.Hilbert空间上依范连续的α-次预解算子族[J].应用泛函分析学报,2011,13(2):201-208. |
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| 作者姓名： | 刘茹 李淼 |
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| 作者单位： | 四川大学数学学院,成都,610064 |
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| 摘 要： | 主要运用Laplace-Stieltjes的方法,讨论Hilbert空间上α-次预解算子族的依范连续性与其预解式的关系,得到一个主要结果：Hilbert空间上α-次预解算子族的依范连续性与其预解式在当｜τ｜→∞时,‖（ω＋iτ）~（α-1）R（（ω＋iτ）~α,A）‖→0等价.
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| 关 键 词： | α-次预解算子族 预解式 依范连续 Laplace-Stieltjes变换 |
Norm-Continuous α-Times Resolvent Families on a Hilbert Space |
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| LIU Ru,LI Miao.Norm-Continuous α-Times Resolvent Families on a Hilbert Space[J].Acta Analysis Functionalis Applicata,2011,13(2):201-208. |
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| Authors: | LIU Ru LI Miao |
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| Institution: | LIU Ru,LI Miao Department of Mathematics,Sichuan University,Chengdu 610064,China |
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| Abstract: | The writer mainly use the method of Laplace-Stieltjes transform,discusses the relationshipbetween the norm-continuity ofα-times resolvent family S_α（t） and it＇s resolvent on a Hilbert space,obtains a main result that the norm-continuity ofα-times resolvent family is equivalent to ｜｜（ω＋iT）~（α-1）R（（ω＋ iT）~α,A） ｜｜→0 as ｜T｜→∞on a Hilbert space |
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| Keywords: | α-times resolvent family resolvent norm-continuous Laplace-Stieltjes transform |
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