带有非局部边界条件的Dirac算子的迹

带有非局部边界条件的Dirac算子的迹

论文摘要

记方程称为一维Dirac方程。本文研究了它带有非局部边界的特征值问题的迹公式。其边界条件如下:首先利用Dirac方程初值问题解的渐近估计,构造了一个整函数ω(λ),其零点集合与带有非局部边界条件的Dirac特征值问题的特征值集重合。然后借助于一个恒等式:采用留数方法,对Dirac算子的特征值进行了估计,得到了两个边值问题的特征值的渐近迹公式。

论文目录

  • 中文摘要
  • Abstract
  • §1 引言
  • §2 问题(Ⅰ)决定特征值的整函数
  • §3 问题(Ⅰ)的迹
  • §4 问题(Ⅱ)决定特征值的整函数
  • §5 问题(Ⅱ)的迹
  • 参考文献
  • 致谢
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    带有非局部边界条件的Dirac算子的迹
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