This monograph gives access to the theory of continuous linear representations of general real Lie groups to readers who are already familiar with the rudiments of functional analysis and Lie groups. The first half of the book is centered around the relation between a continuous linear representation (of a Lie group over a Banach space or even a more general space) and its tangent; the latter is a Lie algebra representation in a sense. Starting with the Hille-Yosida theory, quite recent results are reached. The second half is more standard unitary theory with applications concerning the Galilean and Poincaré groups. Appendices help readers with diverse backgrounds to find the precise descriptions of the concepts needed from earlier literature. Each chapter includes exercises.

Table of Contents

1. The Hille-Yosida Theory. 2. Convolution and Regularization. 3. Smooth Vectors. 4. Analytic Mollifying. 5. The Integrability Problem. 6. Compact Groups. 7. Commutative Groups. 8. Induced Representations. 9. Projective Representations. 10. The Galilean and Poincaré Groups.

Appendix: A. Topology. B. Measure and Integration. C. Functional Analysis. D. Analytic Mappings. E. Manifolds, Distributions, Differential Operators. F. Locally Compact Groups, Lie Groups. References. Index.


No. of pages:
© 1992
North Holland
Print ISBN:
Electronic ISBN:

About the editor

Z. Magyar

Affiliations and Expertise

Mathematical Institute of the Hungarian Academy of Sciences, Budapest, Hungary


@from:P.E.T. Jørgensen @qu:...well written and addressed to graduate students and researchers alike... Each chapter ends with a collection of excellent exercises... @source:Mathematical Reviews @qu:Well written and carefully organized... valuable both for mathematicians and physicists with interests in the field. @source:European Mathematical Society Newsletter