1999/06/29 by Andrew Hassell, Hassell, Andrew, András Vasy +2
Mathematics · #35P25 (Primary) 58G15 #35S30 #58G25 (Secondary) #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.AP #math.DG #msc:35P25 #msc:35S30 #msc:58G15 #msc:58G25
paper · pdf · doi:10.48550/arxiv.math/9906206
45 pages, 2 figures, AMS Latex; to appear in Journal d'Analyse Mathematique
arxiv created 1999/06/29 · openalex publication_date 1999/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.