Abstract Harmonic Analysis [electronic resource] : Volume II: Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups / by Edwin Hewitt, Kenneth A. Ross
Imprint
Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1970
This book is a continuation of Volume I of the same title [Grundยญ lehren der mathematischen Wissenschaften, Band 115 ]. We constantly 1 1. The textbook Real and cite definitions and results from Volume abstract analysis by E. HEWITT and K. R. STROMBERG [Berlin ยท Gottinยญ gen ยทHeidelberg: Springer-Verlag 1965], which appeared between the publication of the two volumes of this work, contains many standard facts from analysis. We use this book as a convenient reference for such facts, and denote it in the text by RAAA. Most readers will have only occasional need actually to read in RAAA. Our goal in this volume is to present the most important parts of harmonic analysis on compact groups and on locally compact Abelian groups. We deal with general locally compact groups only where they are the natural setting for what we are considering, or where one or another group provides a useful counterexample. Readers who are interested only in compact groups may read as follows: ยง 27, Appendix D, ยงยง 28-30 [omitting subheads (30.6)-(30.60)ifdesired], (31.22)-(31.25), ยงยง 32, 34-38, 44. Readers who are interested only in locally compact Abelian groups may read as follows: ยงยง 31-33, 39-42, selected Misยญ cellaneous Theorems and Examples in ยงยง34-38. For all readers, ยง 43 is interesting but optional. Obviously we have not been able to cover all of harmonic analysis
CONTENT
Seven: Representations and duality of compact groups -- Eight: Fourier transforms -- Nine: Analysis on compact groups -- Ten: Spectral synthesis -- Eleven: Miscellany -- Appendix D: Tensor products and von Neumann norms -- Appendix E: Miscellaneous facts from functional analysis -- Addendum to Volume I -- Index of symbols -- Index of authors and terms
