Low Energy Limit for the Resolvent of Some Fibered Boundary Operators

For certain Dirac operators $$\eth _{\phi }$$ associated to a fibered boundary metric $$g_{\phi , we provide pseudodifferential characterization of the limiting behavior $$(\eth }+k\gamma )^{-1}$$ as $$k\searrow 0$$ where $$\gamma $$ is self-adjoint operator anti-commuting with and whose square identity. This yields in particular low energy limit resolvent }^2$$ generalizing result Guillarmou Sher about Hodge Laplacian an asymptotically conical metric. As application, use our give inverse some suspended version . One important ingredient proof main theorem that Fredholm when acting on suitable weighted Sobolev spaces. has been known experts for time take this occasion complete explicit proof.