一类四阶Hamilton算子特征值的代数指标

Algebraic Index of Eigenvalues of a Class of Fourth-Order Hamiltonian Operator

研究了一类四阶Hamilton算子H_A特征值的代数指标问题.根据算子A与Hamilton算子H_A的关系,讨论了Hamilton算子H_A特征值的几何重数,代数指标及代数重数.最后结合例子说明其结果的有效性.

In this paper, the algebraic index of eigenvalues of a class of fourth-order Hamilton operators is studied. According to the relationship between the Hamiltonian operator HA and the operator A, we derived the geometric multiplicity, algebraic index and algebraic multiplicity of the eigenvalue of the Hamilton operator HA. Finally, combining with the example to illustrate the effectiveness of the results.