| 刘茹,李淼.Hilbert空间上$\alpha$-次预解算子族的生成元特征[J].数学研究及应用,2011,31(3):420~428 |
| Hilbert空间上$\alpha$-次预解算子族的生成元特征 |
| Characteristic Conditions for the Generation of $\alpha$-Times Resolvent Families on a Hilbert Space |
| 投稿时间：2009-07-08 修订日期：2010-04-26 |
| DOI：10.3770/j.issn:1000-341X.2011.03.005 |
| 中文关键词: $\alpha$-次预解算子族 预解式 秩-1扰动 相对有界扰动. |
| 英文关键词:$\alpha$-times resolvent family resolvent rank-1 perturbation relatively-bounded perturbation. |
| 基金项目:国家自然科学基金(Grant No.10971146). |
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| 中文摘要: |
| 2000年, 史东华和冯德兴给出了在Hilbert空间上生成$C_0$半群的特征条件.本文将这个条件拓展到$\alpha$-次预解算子族上, 并用此条件证明了$\alpha$-次预解算子族的秩-1扰动定理和相对有界扰动定理. |
| 英文摘要: |
| In 2000, Shi and Feng gave the characteristic conditions for the generation of $C_0$-semigroups on a Hilbert space. In this paper, we will extend them to the generation of $\alpha$-times resolvent operator families. Such characteristic conditions can be applied to show rank-1 perturbation theorem and relatively-bounded perturbation theorem for $\alpha$-times resolvent operator families. |
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