Acoustic Waves in Perturbed Stratified Fluids: A Spectral Theory

The acoustic wave propagator in perturbed stratified fluids is given by where the speed of sound c and the density ρ are short-range perturbations of one-dimensional functions. It is shown that H is spectrally absolutely continuous (its spectrum is [0, ∞)) except possibly for a sequence of (positive) eigenvalues, which can accumulate only at 0, ∞. A "limiting absorption principle" for H, including thresholds, is established between suitably weighted L2 spaces. The limiting values of the resolvent are shown to be Hölder continuous.