Wallach N.R. Symplectic Geometry and Fourier Analysis

2nd ed. — New York: Dover Publications, 2018. — 264 p. — (Dover Books on Mathematics). — ISBN 9780486816890.This book derives from author Nolan R. Wallach's notes for a course on symplectic geometry and Fourier analysis, which he delivered at Rutgers University in 1975 for an audience of graduate students in mathematics and their professors. The monograph is geared toward readers who have taken a basic course in differential manifolds and elementary functional analysis. The first chapters cover certain geometric preliminaries, advancing to discussions of symplectic geometry and the application of its concepts to the action of a Lie group on a symplectic manifold. Subsequent chapters address Fourier analysis, the metaplectic representation, and quantization. A final chapter on the Kirillov theory applies the ideas of the previous chapters to homogeneous symplectic manifolds of nilpotent Lie groups. The book concludes with an Appendix on Quantum Mechanics by Robert Hermann.This Dover edition, first published in 2017, is a revised and corrected republication of the work originally published in 1977 by Math Sci Press, Brookline, Massachusetts, as Volume V in the series “Lie Groups: History, Frontiers and Applications.”True PDF