非自伴Dirac算子的迹公式

Trace Identities of Non-Self-Adjoint Dirac Operators

中文关键词:  Dirac算子  整函数  留数方法  迹公式.

英文关键词:Dirac operator  eigenvalue  residue method  trace identity.

中文摘要:

      本文研究了非自伴Dirac算子的一般两点边值问题的渐近迹. 首先运用平移算子得到了其Cauchy问题解的渐近式, 并由此及边界条件, 构造了整函数$\omega(\lambda)$, 利用它将边界条件分为八种基本类型, 最后采用留数的方法, 得到了四种主要类型的特征值的渐近迹公式.

英文摘要:

      This paper deals with asymptotic trace of non-self-adjoint Dirac operator eigenvalue problem with two points linear boundary condition. The asymptotic eatimations of solution of Cauchy problem are obtained for Dirac equation by use of the transformation matrix operator. By constructing an entire function $\omega(\lambda)$, and discussing every term's coefficient of $\omega(\lambda)$, boundary conditions are turned into eight element types. By resorting the residue method, four types eigenvalue's trace identities are obtained.