Diffraction and Scattering on Product Cones

Mengxuan Yang

Published 2020-04-15Version 1

We prove a propagation of polyhomogeneity of the diffractive wave and relate the scattering matrix to the diffraction coefficient, which is the leading symbol of the diffractive half wave kernel, on product cones. We first conclude that diffractive waves enjoy a one-step polyhomogeneous property on product cones, which is an improvement of Cheeger-Taylor's classical result of half-step polyhomogeneity of diffractive wave in [CT82a], [CT82b]. We also conclude that on product cones, the scattering matrix is the diffraction coefficient for strictly diffractively related points on cross sections, which is a generalization of Ford, Hassell and Hillairet's result of 2-dimensional flat cone settings [FHH18]. In the last section, we also give a radiation field interpretation of the relationship between the scattering matrix and the diffraction coefficient.