Estimates for wave propagation in inhomogenous acoustic media

AbstractThis work answers a number of questions about the relationship between time-domain and frequency-domain solutions of the acoustic equation. A time-domain Green's function is constructed by a semigroup approach that leads to large-time growth estimates. The Fourier transform of this solution is also a solution of the Lippmann-Schwinger equation; this connection shows how to interpret the the delta functions that arise in the time-domain theory