THE SEPARABILITY THEOREM IN TERMS OF DISTRIBUTIONS WITH DISCUSSION OFELECTROMAGNETIC SCATTERING-THEORY

The separability theorem states that, given a linear partial different ial equation and special coordinates allowing to find a family of sepa rated solutions, all solutions of physical interest of the equations c an be obtained from linear combinations of the separated solutions. In developing the theory of interaction between an infinite cylinder and a Gaussian beam, it has been recently observed that the theorem may f ail in terms of functions. In this paper, it is shown that the separab ility theorem is recovered if solutions are expressed in terms of dist ributions instead of in terms of functions. Relevance to light scatter ing theory is discussed. (C) 1996 American Institute of Physics.