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Topological groups. Lie groups --- Locally compact groups --- Representations of groups --- Harmonic analysis --- Harmonic analysis. --- Locally compact groups. --- Representations of groups. --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Compact groups --- Topological groups --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groupes topologiques --- Groupes localement compacts --- Representation

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This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, Euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are more demanding.This text grew out of lectures which the author gave at the N.S.F. Advanced Science Seminar on Algebraic Groups at Bowdoin College in 1968.

Topological groups. Lie groups --- Lie algebras --- Representations of groups --- Representations of algebras --- Algèbres de Lie --- Représentations de groupes --- Représentations d'algèbres --- #TCPW W2.0 --- #TCPW W2.1 --- Algebra --- Group representation (Mathematics) --- Groups, Representation theory of --- Group theory --- Algebras, Lie --- Algebra, Abstract --- Algebras, Linear --- Lie groups --- Lie algebras. --- Representations of groups. --- Representations of Lie algebras. --- Representations of Lie groups. --- Algèbres de Lie --- Représentations de groupes --- Représentations d'algèbres --- Representations of Lie algebras --- Lie, Algèbres de