General theorems relating to wave propagation governed by self-adjoint and Hermitian self-adjoint differential operators of order 2r

Abstract
When plane waves are partly reflected and transmitted from a medium differing from free space, various conditions ensure the existence of simple identities between the reflexion and transmission coefficients. When differential equations of order In govern wave propagation, conditions to be placed both upon the generalized medium and upon the generalized waves are investigated so as to ensure the existence of exact analogues to these elementary identities. The theory is developed in terms of selfadjoint and Hermitian self-adjoint differential operators of order 2 The results fallout from the canonical forms for various skew-Hermitian and skew-symmetric matrices J with complex elements, unitary and orthogonal matrices being found so that J should be unitarily and/or orthogonally similar to its appropriate canonical forms.

This publication has 5 references indexed in Scilit: