Pseudo-differential operators for embedding formulae

Abstract

A new method is proposed for deriving embedding formulae in 2D diffraction problems. In contrast to the approach developed in Craster and Shanin (2005) [7], which is based on a differential operator, here a pseudo-differential, i.e., a non-local operator is applied to the wave field. Using this non-local operator a new embedding formula is derived for scattering by a single wedge. The formula has uniform structure for all opening angles, including angles irrational with respect to π ; the earlier theory, Craster and Shanin (2005) [7], was valid only for rational angles.