关于J-对称微分算子的若干问题

On Some Problems of J—symmetric Differential Operators

本文给出了具充分光滑系数的J-对称微分算式的一般形式;证明了J-对称微分算式τ和对称微分算式^+τ的亏指数之间的一个关系式d(τ^+τ)>2d(樱;讨论了当J-对称微分算式τ的系数是实值函数时,此时它又是对称的,由它所生成的自伴算子和J-自伴算子之闻的关系,给出了既是自伴的又是J-自伴的边条件的完全描述;最后举了一个二阶极限点的微分算式的例,具体给出了其全部的J-自伴域的描述。

In this paper we give the general form of J-symmetric differential expressions with suffieiently smooth eoeffieients and prove the inequality d(t+t)≥2d(t). Then we give the characterization of the domain which is both selfadjoint and J- selfadjoint for the J-symmetrie differential expression with real coeffieients. Finally, we give all the J-selfadjoint domains of second order differential expression t=-D^2+i which is in the limit point case.