Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory

This book is probably best (at least in 1987) viewed as an introduction to the theory of unitary representations of locally compact groups, with the Heisenberg group as a basic example. The author gives the basis of representation theory, the theory of square-integrable representations, and the Mackey "little group'' method for determining the unitary dual of a group (the last-mentioned in a simplified setting and without some proofs). He applies these results to prove the Stone-von Neumann theorem and the theorem of Kirillov identifying the dual of a nilpotent Lie group. The Heisenberg group receives detailed attention. In the final chapter, he applies representation theory on the Heisenberg group to the subject of radar ambiguity functions and radar signal design, a topic on which the author has written several papers. The book is clearly written, with few misprints, and should be easily accessible to a second-year graduate student.