共查询到16条相似文献,搜索用时 562 毫秒
1.
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. 相似文献
2.
将点谱划分为四个部分,得到上三角无穷维Hamilton算子的点谱σ_p(H)关于虚轴对称的充要条件.在此基础上,结合无穷维Hamilton算子的谱结构,得到无穷维Hamilton算子剩余谱的完全描述,从而实现了利用其内部算子刻画剩余谱. 相似文献
3.
4.
5.
只有纯虚谱的Hamilton算子 总被引:1,自引:1,他引:0
刻画了一类无穷维Hamilton算子的谱的分布情况,并得到了无穷维Hamilton算子只有纯虚谱的充分条件.最后,构造出具体的例子以说明判别准则的有效性. 相似文献
6.
7.
8.
以Hamilton算子的数值域为基础,研究了一类算子的二次数值域关于实轴,虚轴的对称性.此外从α-J-自伴算子的n次数值域关于过原点直线对称出发,得到了有界Hamilton算子的一类n次数值域关于虚轴的对称性. 相似文献
9.
该文得到了一类无穷维Hamilton算子的剩余谱和点谱存在的几个判别准则,从而给出了求其剩余谱和点谱的方法. 在此基础上构造了L^2*L^2中无穷维Hamilton算子的剩余谱非空的具体例子, 从而进一步验证了判别准则的有效性. 相似文献
10.
L2×L2中的一类无穷维Hamilton算子的剩余谱 总被引:3,自引:0,他引:3
该文得到了一类无穷维Hamilton算子的剩余谱和点谱存在的几个判别准则,从而给出 了求其剩余谱和点谱的方法.在此基础上构造了L2×L2中无穷维Hamilton算子的剩余谱 非空的具体例子,从而进一步验证了判别准则的有效性. 相似文献
11.
本文研究斜对角无穷维Hamilton算子$H=\begin{pmatrix}0&B\\C&0\end{pmatrix}$的点谱和特征函数系辛结构的非退化性, 给出斜对角无穷维Hamilton算子$H$的特征函数系具有非退化辛结构的充分必要条件. 基于此, 进一步刻画了斜对角无穷维Hamilton算子$H$的点谱分别包含于实轴、虚轴以及其它区域的充分必要条件. 最后, 以板弯曲问题和弦振动问题中导出的斜对角无穷维Hamilton算子为例, 验证了所得结论的正确性. 相似文献
12.
The spectral properties of the off-diagonal infinite-dimensional Hamiltonian operator are studied in this article. Characterizations of the spectrum, the point spectrum and the residual spectrum are given. A spectral inclusion property of numerical range is proved. 相似文献
13.
This paper deals with the structure of the spectrum of infinite dimensional Hamiltonian operators.It is shown that the spectrum,the union of the point spectrum and residual spectrum,and the continuous spectrum are all symmetric with respect to the imaginary axis of the complex plane. Moreover,it is proved that the residual spectrum does not contain any pair of points symmetric with respect to the imaginary axis;and a complete characterization of the residual spectrum in terms of the point spectrum is then given.As applications of these structure results,we obtain several necessary and sufficient conditions for the residual spectrum of a class of infinite dimensional Hamiltonian operators to be empty. 相似文献
14.
15.
证明了一类乘积算子点谱的对称性并将其应用到Hamilton算子、反Hamilton算子上,最后举例说明了乘积算子数值域的一些性质. 相似文献
16.
Block numerical ranges of matrix polynomials, especially the quadratic numerical range, are considered. The main results concern spectral inclusion, boundedness of the block numerical range, an estimate of the resolvent in terms of the quadratic numerical range, geometrical properties of the quadratic numerical range, and inclusion between block numerical ranges of the matrix polynomials for refined block decompositions. As an application, we connect the quadratic numerical range with the localization of the spectrum of matrix polynomials. 相似文献