| Riesz半群母元广义本征函数系统的完整性 |
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| 引用本文： | 许跟起,王胜华.Riesz半群母元广义本征函数系统的完整性[J].数学学报,1996,39(2):263-267. |
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| 作者姓名： | 许跟起 王胜华 |
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| 作者单位： | 山西大学数学系，江西上饶师专 |
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| 摘 要： | 本文在可分的Ｂａｎａｃｈ空间研究Ｒｉｅｓｚ半群无穷小母元广义本征函数系统的完整性，利用母元的予解式和谱分布，我们给出予解式的级为有限时广义本征函数系统完整性的判定．
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| 关 键 词： | Riesz半群，无穷小母元，广义本征函数，完整性 |
| 收稿时间： | 1994-4-4 |
| 修稿时间： | 1994-12-16 |
The Completeness of Generalised Eigenfunction of a Class of Infinitesimal Generators of Riesz Semigroups |
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| Xu Genqi.The Completeness of Generalised Eigenfunction of a Class of Infinitesimal Generators of Riesz Semigroups[J].Acta Mathematica Sinica,1996,39(2):263-267. |
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| Authors: | Xu Genqi |
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| Affiliation: | Xu Genqi(Department of Mathematics, Shanxi University, Taiyuan 030006, China)Wang Shenghua(Department of Mathematics, Shangrao Teacher's Collage, Shangrao 334000, China) |
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| Abstract: | In this paper we study the completeness of system of generalized eigenfunctions of A, which is the infinitesimal generator of a Riesz semigroup in a separable Banach space. In view of the resolvent and the spectral distribution of A, we present the criterion of completeness of system of generalized eigenfunction of A with resolvent of order p < +∞. |
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| Keywords: | Riesz semigroup infinitemsimal generator generalized eigenfunction completeness |
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