【作者】 郭芳；

【导师】 孙炯；

【作者基本信息】 内蒙古大学 ， 基础数学， 2005， 硕士

【摘要】 对称微分算子理论中自共轭域的描述,是微分算子理论中的基础问题之一,常型的问题在五十年代已得到解决,五十余年来人们更多的注意力放在奇型微分算子自共轭边界条件的描述上。本文研究了无穷区间上二阶、高阶奇型微分算子的辛结构,利用最大与最小算子域构造了一个辛空间,用辛空间中的线性流形来刻画定义在无穷区间上二阶、高阶奇型对称微分算子的自共轭扩张问题。给出了与微分算子自共轭域相对应的Lagrangian子流形的描述和分类情况。更多还原

【Abstract】 The discription of the self-adjoint domains of differential operators is one of the basic questions.The results of ordinary differential operators have been obtained in 50s’.Scientists’ attention is paid to the discription of the self-adjoint boundary condi-tions of singular differential operators during 50 years recently. In this paper,we build symplectic structure of 2-nd order and high order singular differential operators on infinite interval, we construct a symplectic space by the maximal and minimal operator domain . Using Lagrangian submanifold in symplectic space ,we give a complete discription and classification of the self-adjoint domains of the 2-nd order and high order singular differential operators on infinite interval .更多还原