Spectra of Off-diagonal Infinite-Dimensional Hamiltonian Operators and Their Applications to Plane Elasticity Problems

在现在的纸，离开斜的无限维的 Hamiltonian 操作员的系列被学习。起初，我们证明光谱，连续光谱，并且点光谱的联合和操作员的剩余光谱关于真实的轴和想象的轴是对称的。然后为减少学习问题的尺寸的目的，操作符的系列被二个自我伴随操作符的产品的系列在州的空格表示。最后，上述结果被用于飞机弹性问题，它显示出结果的有实行可能。

In the present paper, the spectrums of off-diagonal infinite-dimensional Hamiltonian operators are studied. At first, we prove that the spectrum, the continuous-spectrum, and the union of the point-spectrum and residual- spectrum of the operators are symmetric with respect to real axis and imaginary axis. Then for the purpose of reducing the dimension of the studied problems, the spectrums of the operators are expressed by the spectrums of the product of two self-adjoint operators in state spac,3. At last, the above-mentioned results are applied to plane elasticity problems, which shows the practicability of the results.