The spectral projections and the resolvent for scattering metrics

Details The spectral projections and the resolvent for scattering metrics The spectral projections and the resolvent for scattering metrics

1999-06-29

arxiv.org/abs/math/9906206v1

Mathematics

Analysis of PDEs

45 pages, 2 figures, AMS Latex; to appear in Journal d'Analyse Mathematique

Scientific paper

In this paper we consider certain asymptotically Euclidean spaces, namely compact manifolds with boundary X equipped with a scattering metric g, as defined by Melrose. We then consider Hamiltonians H which are `short-range' self-adjoint perturbations of the Laplacian of g. Melrose and Zworski have given a detailed description of the associated scattering matrix and Poisson operator as a Fourier integral operator and a (singular) Legendre distribution respectively. In this paper we describe the kernel of the spectral projections and the boundary value of the resolvent at the real axis. We define classes of Legendre distributions on certain types of manifolds with corners, and show that the kernels of the spectral projection and the resolvent are in these classes. We also discuss some applications of these results.

Affiliated with

Also associated with

No associations

Rating

The spectral projections and the resolvent for scattering metrics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The spectral projections and the resolvent for scattering metrics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The spectral projections and the resolvent for scattering metrics will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-422501