Eigenfunction expansions for wave propagation problems in classical physics

The eigenfunction expansion theorem is proved for a class of matrix partial differential operators which arises in the study of wave propagation phenomena of classical physics. Our result is a generalization of the results of Wilcox and all (Arch. Rational Mech. Anal. 46 280 (1972)). The most significant generalization is the relaxation of the ''uniform propagativity'' condition (which is quite restrictive from the physical point of view) up to ''constant deficit'' property