弹性理论中上三角无穷维Hamilton算子根向量组的完备性

考虑弹性力学中一类上三角无穷维 Hamilton 算子．首先,给出此类Hamilton算子特征值的几何重数和代数指标,进而得到代数重数．其次,根据Hamilton算子特征值的代数重数确定其特征(根)向量组完备的形式,得到此类Hamilton算子特征(根)向量组的完备性是由内部算子特征向量组决定．最后,将所得结果应用到弹性力学问题中．

Completeness of the System of Root Vectors of Upper Triangular Infinite-Dimensional Hamiltonian Operators Appearing in Elasticity Theory

A class of upper triangular infinite-dimensional Hamiltonian operators appearing in elasticity theory was dealt with.The geometric multiplicity and algebraic index of the eigenvalue were investigated, then further the algebraic multiplicity of the eigenvalue was obtained. Based on these properties, the concrete completeness formulation of the system of eigen or root vectors of the Hamiltonian operator was proposed.It is shown that this completeness is determined by the system of eigenvectors of its operator entries.Finally,some illustrating applications from elasticity theory are presented.