Abstract Harmonic Analysis de Edwin Hewitt

Abstract Harmonic Analysis: Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups: Grundlehren der mathematischen Wissenschaften, cartea 152

Edwin Hewitt

Kenneth A. Ross

This book is a continuation of vol. I (Grundlehren vol. 115, also available in softcover), and contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups. From the reviews: "This work aims at giving a monographic presentation of abstract harmonic analysis, far more complete and comprehensive than any book already existing on the subject...in connection with every problem treated the book offers a many-sided outlook and leads up to most modern developments. Carefull attention is also given to the history of the subject, and there is an extensive bibliography...the reviewer believes that for many years to come this will remain the classical presentation of abstract harmonic analysis." Publicationes Mathematicae

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Specificații

ISBN-13: 9783540583189
ISBN-10: 3540583181
Pagini: 784
Ilustrații: X, 771 p.
Dimensiuni: 155 x 235 x 41 mm
Greutate: 1.08 kg
Ediția:1st ed. 1970. 2nd printing 1994
Editura: Springer Berlin, Heidelberg
Colecția Springer
Seria Grundlehren der mathematischen Wissenschaften

Locul publicării:Berlin, Heidelberg, Germany

Cuprins

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.