Linear Analysis and Representation Theory

A frequently cited scholarly text, this unified treatment constitutes an ideal reference for graduate math students and mathematicians. Its clear, accurate formulations offer a relatively self-contained resource for those studying locally compact groups, Lie groups and algebras, harmonic analysis, and the representation of groups. An introductory chapter on algebras and Banach algebras is followed by a summary of linear functional analysis and examinations of spectral theorem, stable subspaces, and von Neumann algebras. Subsequent chapters explore elementary representation theory in Hilbert space; topological groups, invariant measures, convolutions, and representations; the basic theory of induced representations; and fundamentals of the theory of representations of compact groups. The final chapters offer a concise introduction to the theory of Lie algebras, Lie groups, and transform groups.