二次算子族及非负无穷维Hamilton算子的谱分布  

The Scatter of Spectrum of Quadratic Operator Pencil and Nonnegative Infinite Dimensional Hamiltonian Operator

作　　者：邢利刚[1,2] 阿拉坦仓[3] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]内蒙古财经学院统计与数学学院,呼和浩特010051 [3]内蒙古大学数学科学学院,呼和浩特010021

出　　处：《数学学报（中文版）》2012年第4期665-672,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(10962004)

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）=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．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 spectrumof 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 

分 类 号：O175.3[理学—数学]