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)=λ2M-iλK-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.
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.
关键词
无穷维Hamilton 算子 /
二次算子族 /
谱
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Key words
infinite-dimensional Hamiltonian operators /
quadratic operator pencils /
spectrum
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参考文献
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[5] Wu D. Y., Alatancang, Completeness in the sense of Cauchy principle value of the eigenfunction systems ofinfinite dimensional Hamiltonian operator, Sci. China Ser. A, Math., 2008, 38(8): 904-912 (in Chinese).
[6] Pivovarchik V. N., On Spectrum of A certain class of Quadratic operator pencils with one-dimensional linearpart, Ukrainian Mathematical Journal, 2007, 59(5): 766-781.
[7] Kato Dr. T., Perturbation Theory for Linear Operators, Springer-Verlag, New York, 1966.
[8] Sun J., Wang Z., Spectrum Analysis of Linear Operator, Science Press, Beijing, 2005 (in Chinese).
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脚注
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基金
国家自然科学基金资助项目(10962004)
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