Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)

First Advisor

Jerome A. Goldstein


This thesis is concerned with new mathematical contributions to this area of mathematical physics. It consists of two parts. The first part discusses Pauli uniqueness problem in the content of locally compact abelian groups. We get improved results for $R\sp{n}$, new results for $T\sp{n}$ and $Z\sb{n}$. In the second part which is the main part of the thesis, we develop a new approach to the scattering for Nth order factored equations based on an abstract version of d'Alembert's formula. We show that the asymptotic equivalence (or scattering theory) of the pair of higher order factored equations reduces to the asymptotic equivalence of the first order equations. Our approach is clean, direct and easy to use. It also enables us to recover and unify old results on acoustic waves as well as to obtain new results on elastic waves. Moreover, it follows from our approach that elastic wave theory is a corollary of the acoustic wave theory.