Author | Hewitt, Edwin. author |
---|---|
Title | Abstract Harmonic Analysis [electronic resource] : Volume 1: Structure of Topological Groups Integration Theory Group Representations / by Edwin Hewitt, Kenneth A. Ross |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1963 |
Connect to | http://dx.doi.org/10.1007/978-3-662-00102-8 |
Descript | online resource |
One: Preliminaries -- Section 1. Notation and terminology -- Section 2. Group theory -- Section 3. Topology -- Two: Elements of the theory of topological groups -- Section 4. Basic definitions and facts -- Section 5. Subgroups and quotient groups -- Section 6. Product groups and projective limits -- Section 7. Properties of topological groups involving connectedness -- Section 8. Invariant pseudo-metrics and separation axioms -- Section 9. Structure theory for compact and locally compact Abelian groups -- Section 10. Some special locally compact Abelian groups -- Three: Integration on locally compact spaces -- Section 11. Extension of a linear functional and construction of a measure -- Section 12. The spaces Lp (X) (1 ? p ? ?) -- Section 13. Integration on product spaces -- Section 14. Complex measures -- Four: Invariant functionals -- Section 15. The Haar integral -- Section 16. More about Haar measure -- Section 17. Invariant means defined for all bounded functions -- Section 18. Invariant means on almost periodic functions -- Five: Convolutions and group representations -- Section 19. Introduction to convolutions -- Section 20. Convolutions of functions and measures -- Section 21. Introduction to representation theory -- Section 22. Unitary representations of locally compact groups -- Six: Characters and duality of locally compact Abelian groups -- Section 23. The character group of a locally compact Abelian group -- Section 24. The duality theorem -- Section 25. Special structure theorems -- Section 26. Miscellaneous consequences of the duality theorem -- Appendix A: Abelian groups -- B: Topological linear spaces -- C: Introduction to normed algebras -- Index of symbols -- Index of authors and terms