The evolution of applied harmonic analysis. Models of the real world. With forewords by Ronald Bracewell and Dušan Zrnić (Q310898)

This is the second edition of [Zbl 1064.43001], which presents an overview about the long-standing evolution of the applications of Harmonic Analysis to other sciences than mathematics. The main difference on this second edition is the addition of a new chapter ten specially devoted to applications to atmospheric science. It deals with turbulence, sodar, radar, lidar, and climate, considering their interrelations both from technical and historical perspectives. Special attention is devoted to the phenomenon of turbulence and consequent use of Navier-Stokes equations and Kolmogorov theory, as well as to the physical process of the interaction of acoustic waves with turbulence. Other processes like the Doppler effect, and how to calculate the Doppler shift for sodar and for radar are explained with enough detail, and also in a somehow compromised way which is even profitable for readers outside those specific areas. In this sense, this last new chapter ten is in line with the previous ones, showing a compromise between an introductory technical exposition to several topics of atmospheric science and a historical reference to their corresponding discoveries. This choice keeps the reader's interest at a high level by allowing cross connections with the evolution of the applicability of Harmonic Analysis throughout the years.