关于J－对称微分算子的J－自伴扩张的若干注记  

Some Notes on J-Selfadsoiot Extensions of J-Symmetric Ordinary Differential Operators

作　　者：尚在久 

机构地区：[1]中国科学院数学研究所

出　　处：《数学学报（中文版）》1996年第3期387-395,共9页Acta Mathematica Sinica：Chinese Series

摘　　要：本文给出了一条解析描述Ｊ－对称微分算子Ｊ－自伴扩张的新途径．我们借助方程Ｔ（ｙ）＝λｏｙ的解，而不是如文［３］利用方程＋（ｙ）＇＝－ｙ的解来描述Ｊ－对称微分算式的所有Ｊ－自伴域在奇异端点的边条件，不过我们假设生成的最小算子具非空正则域．我们对主要定理给出了若干有趣的注，得到了二阶极限圆情形的有趣结果．In this papert we provide a new way to analytically describe all of the J-selfadjoint edensions of J-symmetric ordinary differential operators associated with any J-symmetric differential expression γ by means of the solutions of the equation r(y) =λoy, instead of the solutions of the equation γ+γ(y) = -y as done in [4], under the assumption that the regularity field Π(TO),of the minimal operator To generated by T, is nonempty. Some interesting notes on the main theorem are given. Complete descriptions of J-seifadjoint domains of second order J-symmetric differential expressions with limit-circle are obtained.

关 键 词：J-自伴域 J-对称微分算子 微分算子 J-自伴扩张 

分 类 号：O175.3[理学—数学]