论文标题
某些光纤边界操作员的分解的低能极限
Low energy limit for the resolvent of some fibered boundary operators
论文作者
论文摘要
For certain Dirac operators $ð_ϕ$ associated to a fibered boundary metric $g_ϕ$, we provide a pseudodifferential characterization of the limiting behavior of $(ð_ϕ+kγ)^{-1}$ as $k\searrow 0$, where $γ$ is a self-adjoint operator anti-commuting with $ð_ϕ$ and whose square is the identity.这尤其产生了$ ð_ϕ^2 $的低能量限制的假差表征，从而使Guillarmou和Sher的结果概述了无渐近的圆锥形度量的Hodge Laplacian的低能限制。作为一个应用程序，我们使用结果给出了某些悬挂版本的$ ð_ϕ $的悬挂版本的伪差表征。在我们主要定理证明的证明中，一种重要的成分是，狄拉克运算符$ ð_ϕ $是在适当加权的索博莱夫空间上作用时的弗雷德·霍尔姆（Fredholm）。专家已经知道这个结果已有一段时间了，我们将其作为提供完整的明确证明的机会。
For certain Dirac operators $ð_ϕ$ associated to a fibered boundary metric $g_ϕ$, we provide a pseudodifferential characterization of the limiting behavior of $(ð_ϕ+kγ)^{-1}$ as $k\searrow 0$, where $γ$ is a self-adjoint operator anti-commuting with $ð_ϕ$ and whose square is the identity. This yields in particular a pseudodifferential characterization of the low energy limit of the resolvent of $ð_ϕ^2$, generalizing a result of Guillarmou and Sher about the low energy limit of the resolvent of the Hodge Laplacian of an asymptotically conical metric. As an application, we use our result to give a pseudodifferential characterization of the inverse of some suspended version of the operator $ð_ϕ$. One important ingredient in the proof of our main theorem is that the Dirac operator $ð_ϕ$ is Fredholm when acting on suitable weighted Sobolev spaces. This result has been known to experts for some time and we take this as an occasion to provide a complete explicit proof.
