波动方程混合边值问题的无穷维Hamilton算子辛特征函数系的完备性  

Completeness of Symplectic Eigenfunction System of Infinite Dimensional Hamiltonian Operators of Wave Equation with Mixed Boundary Value Problem

作　　者：冯璐[1] 额布日力吐[1] 阿拉坦仓[2] 

机构地区：[1]内蒙古大学数学科学学院,呼和浩特010021 [2]呼和浩特民族学院,呼和浩特010051

出　　处：《内蒙古大学学报（自然科学版）》2017年第3期254-258,共5页Journal of Inner Mongolia University：Natural Science Edition

基　　金：国家自然科学基金(11362011;11371185);内蒙古自然科学基金(2013MS0103)

摘　　要：把波动方程的混合边值问题应用矩阵多元多项式的带余除法化为Hamilton系统,由Hamilton系统导出无穷维Hamilton算子,并计算出此无穷维Hamilton算子的特征值及相应的辛特征函数系.结合辛特征函数系的辛正交性,证明了该辛特征函数系在L^2空间中广义Cauchy主值意义下的完备性.进而给出了Hamilton系统的辛特征函数展开的级数解.To transfer the wave equation with mixed boundary value problem into the Hamiltonian canonical system by Pseudo-division algorithm for matrix multivariable polynomials,the Ham- iltonian operator is enduced. Then the corresponding eigenvalues and the symplectic eigenfunctions are calculated. With the symplectic orthogonality,it is proved that the corresponding symplectic eigenfunction system is complete in the broad sense of Cauchy＇s principle value. The series solution of the original Hamiltonian canonical system is given by the symplectic eigenfunction expansion method.

关 键 词：波动方程 HAMILTON算子 辛特征函数系 完备性 

分 类 号：O175.3[理学—数学]