无穷维Hamilton 算子广义本征函数系的完备性及其在弹性力学中的应用

本文利用无穷维Hamilton 算子的结构特性, 得到由算子的基本本征函数和若当型本征函数构成的广义本征函数系在Cauchy 主值意义下完备的充分必要条件. 进而将结果应用于弹性力学中的板弯曲问题. 相应结论为Hamilton 体系下的分离变量法(弹性力学求解新体系) 提供了理论保证.

Completeness of generalized eigenfunction systems of infinite-dimensional Hamiltonian operators and its application in Elasticity

By using the structural characteristics of the infinite-dimensional Hamiltonian operators,a necessary and sufficient condition is given for generalized eigenfunction systems to be complete in the sense of Cauchy principal value.The above function systems consist of the eigenfunction and Jordan eigenfunction of the operators.Moreover,the result is applied to plate bending problems.The related conclusion offers a theoretical guarantee for the separation of variables in Hamiltonian system（the new systematic methodology for theory of elasticity）.