一类无穷维Hamilton算子谱的刻画

The Spectral Description for a Class of Infinite Dimensional Hamiltonian Operator

本文讨论了一类无穷维Hamilton算子谱问题,由于无穷维Hamilton算子是非自伴的算子矩阵,对它的谱的讨论比较困难,我们利用无穷维Hamilton算子的特殊结构,将无穷维Hamilton算子的谱问题转化为它的元素算子的某种组合的谱问题,得到了一个充分必要条件,在一定程度上简化了该类无穷维Hamilton算子谱的计算.

In this paper, we mainly discuss the spectrum of a class of infinite dimensional Hamiltonian operators. Generally specking, infinite dimensional Hamiltonian operators are non-selfadjoint operator. Because there is not unified method to the spectrum of nonselfadjoint operators, so lots of scholars study the spectrum of non-selfadjoint operators one by one. Recently, infinite dimensional Hamiltonian operators are more and more popular, because of its important application in elasticity, celestial mechanics, aerospace science and etc. The spectrum is an important aspect of the infinite dimensional Hamiltonian operator. So we study the spectrum of a class of infinite dimensional Hamiltonian operators and obtain some necessary and sufficient conditions using its special structure. Infinite dimension Hamiltonian operators are 2 × 2 matrix operator, so we describe its spectrum by its entry operators. This makes easier to some infinite dimension Hamiltonian operators.