Kramers-Kronig dispersion relations for ultrasonic attenuation obeying a frequency power law

In the recent literature concern has been raised regarding the validity of Kramers-Kronig dispersion relations for media with ultrasonic attenuation obeying a frequency power law (α(ω)=α₀|ω|^y). We demonstrate, however, that Kramers-Kronig dispersion relations for application to these types of media are available. We compare the predicted dispersion using the Kramers-Kronig dispersion relation with the measured dispersion for each liquid, and find absolute agreement to better than 1 m/s across the experimentally available bandwidth. We show that the Kramers-Kronig dispersion predictions are identical to those of the time-causal theory. We also relate these dispersion relations to the Paley-Wiener condition, a general restriction on all causal transforms.