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The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.

Lie groups. --- Representations of groups. --- Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Groups, Lie --- Lie algebras --- Symmetric spaces --- Topological groups

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Topological groups. Lie groups --- 512.74 --- Linear algebraic groups --- Algebraic groups, Linear --- Geometry, Algebraic --- Group theory --- Algebraic varieties --- Algebraic groups. Abelian varieties --- 512.74 Algebraic groups. Abelian varieties --- Groupes, Théorie des --- Groupes, Théorie des --- Geometrie algebrique --- Groupes algebriques