Buch, Englisch, Band 115, 525 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 803 g
Volume I: Structure of Topological Groups Integration Theory Group Representations
Buch, Englisch, Band 115, 525 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 803 g
Reihe: Grundlehren der mathematischen Wissenschaften
ISBN: 978-0-387-94190-5
Verlag: Springer
g a largenumberof concrete ex amplesand factsnotavailablein other textbooks.
Zielgruppe
Research
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
- Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
- Interdisziplinäres Wissenschaften Wissenschaften: Allgemeines
- Mathematik | Informatik Mathematik Mathematische Analysis Reelle Analysis
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
Weitere Infos & Material
One: Preliminaries.- Section 1. Notationand terminology.- Section 2. Group theory.- Section 3. Topology.- ChapterTwo: Elementsof thetheoryof 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 topologicalgroups 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.
