| 二次算子族及非负无穷维Hamilton算子的谱分布 |
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| 引用本文： | 邢利刚,阿拉坦仓. 二次算子族及非负无穷维Hamilton算子的谱分布[J]. 数学学报, 2012, 0(4): 665-672 |
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| 作者姓名： | 邢利刚 阿拉坦仓 |
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| 作者单位： | 内蒙古大学数学科学学院;内蒙古财经学院统计与数学学院 |
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| 基金项目： | 国家自然科学基金资助项目(10962004) |
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| 摘 要： | 本文讨论了一类在弦和梁的微小振动中出现的二次算子族L(λ)=λ~2MλK-A的谱分布问题,进而将所得结论与无穷维Hamilton算子联系起来,利用无穷维Hamilton算子的特殊结构,得到了一类非负无穷维Hamilton算子的谱分布,这为无穷维Hamilton算子的半群方法提供了理论保证.
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| 关 键 词： | 无穷维Hamilton算子 二次算子族 谱 |
The Scatter of Spectrum of Quadratic Operator Pencil and Nonnegative Infinite Dimensional Hamiltonian Operator |
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| Affiliation: | Li Gang XING College of Mathematics,Inner Mongolia University,Hohhot 010021,P.R.China College of Statistic and Mathematics,College of Finance and Economics, Hohhot 010051,P.R.China Alatancang College of Mathematics,Inner Mongolia University,Hohhot 010021,P.R.China |
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| Abstract: | In this paper,we discuss the spectrum of a class quadratic operator pencils which appears in vibrations of strings and beams.Meanwhile,we gained the spectrum of the infinite-dimensional Hamiltonian operators making use of these conclusions to the infinite-dimensional Hamiltonian operators and considering the special structure of infinite-dimensional Hamiltonian operators.This provides us with theoretical guarantee to discuss the method of semi-group to the infinite-dimensional Hamiltonian operators. |
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| Keywords: | infinite-dimensional Hamiltonian operators quadratic operator pencils spectrum |
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