George Mackey, The Laplace Transform For Locally Compact Abelian Groups, Proceedings of the National Academy of Sciences of the United States of America Vol. 34, No. 4 (Apr. 15, 1948), pp. 156-162 (jstor:87968)
George Mackey, The Mathematical Foundations of Quantum Mechanics: a Lecture-note Volume, Mathematical physics monograph series, Benjamin (1963), Dover (2004) [google books]
Harmonic analysis as the exploitation of symmetry - a historical survey, Bull. Amer. Math. Soc. (N.S.) Volume 3, Number 1, Part 1 (1980), 543-698 (pdf).
This is reprinted with other essays in
The Scope and History of Commutative and Noncommutative Harmonic Analysis, AMS, 1992.