Pseudo-differential operators

According to Saint Raymond (1991), a pseudo-differential operator is the extension of partial-differential operators as a calculus of polynomial symbols to pseudo-differential operators ($\Psi$DOs) as a calculus of a more general class of symbols which are not necessarily polynomial and which correspond to operators that are not differential. According to the applications section of Saint Raymond (1991), one application is that singularities for the wave equation propagate according to the strong Huygens' principle, at least for the case of three dimensions of space plus one dimension of time.

In Saint Raymond (1991), the theory of $\Psi$DOs is founded on the theory of distributions and the Fourier transform. Also $\Psi$DOs are best applied to elliptic PDEs. <p> Application of $\Psi$DOs to ocean acoustics is described in Jensen et al. (2000).