奇型Dirac算子的谱分析

奇型Dirac算子的谱分析

论文摘要

记B(x)=(?),Q(x)=(?),y(x)=(?)。其中p(x),r(x)是[0,+∞]上的实值连续函数,本文研究下述的奇型Dirac特征值问题:B(x)(dy)/(dx)+Q(x)(?)=λy (1)y1(0)sinα+y2(0)cosα=0,y∈L2(0,+∞)。(2)它等价于一个微分算子的特征值问题。本文由奇型Dirac算子的parseval公式出发,推导证明了parseval反演公式,详尽讨论了奇型Dirac算子谱函数ρ(λ)与谱的关系,最后得出Dirac算子谱的表示

论文目录

  • 摘要
  • Abstract
  • §1 引言
  • §2 谱函数ρ(λ)的存在性
  • §3 Parseval反演公式
  • §4 点款的特征值问题
  • §5 豫解式及其积分表示
  • §6 算子T的谱表示
  • 参考文献
  • 致谢
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    奇型Dirac算子的谱分析
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