Abstract Harmonic Analysis
Subtitle: Volume 1: Structure of Topological Groups Integration Theory Group Representations
By: by Edwin Hewitt, Kenneth A. Ross
Contributors: Ross, Kenneth A., author
Series: Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete -- 115; Die Grundlehren der Mathematischen Wissenschaften, In Einzeldarstellungen mit Besonderer Berücksichtigung der Anwendungsgebiete -- 115.
Publisher: Springer Berlin Heidelberg; Springer
Published: 1963
Place of publication: Berlin, Heidelberg
Language: eng
ISBN-13: 9783662001028; 9783662001042
Subjects: Mathematics; Mathematics, general
Description: When we accepted the kind invitation of Prof. Dr. F. K. SCHMIDT to write a monograph on abstract harmonie analysis for the Grundlehren der Mathematischen Wissenschaften series, we intended to write aH that we could find out about the subject in a text of about 600 printed pages. We intended that our book should be accessible to beginners, and we hoped to make it useful to specialists as weH. These aims proved to be mutuaHy inconsistent. Hence the present volume comprises only half of the projected work. It gives all of the structure of topologie al groups needed for harmonie analysis as it is known to us; it treats integration on locaHy compact groups in detail; it contains an introduction to the theory of group representations. In the second volume we will treat harmonie analysis on compact groups and locally compact Abelian groups, in considerable detail. The book is based on courses given by E. HEWlTT at the University of Washington and the University of Uppsala, although naturally the material of these courses has been enormously expanded to meet the needs of a formal monograph. Like the other treatments of harmonie analysis that have appeared since 1940, the book is a lineal descendant of A. WEIL'S fundamental treatise (WEIL r 4J) 1. The debt of all workers in the field to WEIL'S work is weH known and enormous.
Table of contents: title: One: Preliminaries; title: Section 1. Notation and terminology; title: Section 2. Group theory; title: Section 3. Topology; title: Two: Elements of the theory of topological groups; title: Section 4. Basic definitions and facts; title: Section 5. Subgroups and quotient groups; title: Section 6. Product groups and projective limits; title: Section 7. Properties of topological groups involving connectedness; title: Section 8. Invariant pseudo-metrics and separation axioms; title: Section 9. Structure theory for compact and locally compact Abelian groups; title: Section 10. Some special locally compact Abelian groups; title: Three: Integration on locally compact spaces; title: Section 11. Extension of a linear functional and construction of a measure; title: Section 12. The spaces Lp (X) (1 ? p ? ?); title: Section 13. Integration on product spaces; title: Section 14. Complex measures; title: Four: Invariant functionals; title: Section 15. The Haar integral; title: Section 16. More about Haar measure; title: Section 17. Invariant means defined for all bounded functions; title: Section 18. Invariant means on almost periodic functions; title: Five: Convolutions and group representations; title: Section 19. Introduction to convolutions; title: Section 20. Convolutions of functions and measures; title: Section 21. Introduction to representation theory; title: Section 22. Unitary representations of locally compact groups; title: Six: Characters and duality of locally compact Abelian groups; title: Section 23. The character group of a locally compact Abelian group; title: Section 24. The duality theorem; title: Section 25. Special structure theorems; title: Section 26. Miscellaneous consequences of the duality theorem; title: Appendix A: Abelian groups; title: B: Topological linear spaces; title: C: Introduction to normed algebras; title: Index of symbols; title: Index of authors and terms.