This book is a continuation of Volume I of the same title [Grund-lehren der mathematischen Wissenschaften， Band 115]. We constantly cite definitions and results from Volume l.1 The textbook Real and abstract analysis by E. HEWITT and K. R. STROMBERG [Berlin . Gottingen . Heidelberg: Springer-Verlag 1965]， which appeared between the publication of the two volumes of this work， contains many standaro 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.

《抽象调和分析(第2卷)(英文版)》由休伊特编著，供读者阅读参考。

Preface

Chapter Seven: Representations and duality of compact groups

Section 27. Unitary representations of compact groups

Section 28. More about representations of compact groups

Section 29. Miscellaneous facts about representations

Section 30. The TANNAK-KEIN duality theorem

Chapter Eight. Fourier transforms

Section 31. □ and □ transforms

Section 32. Positive-definite functions and factorization theorems

Section 33. BOCHNER'S theorem

Chapter Nine: Analysis on compact groups

Section 34. Absolutely convergent Fourier series on compact groups

Section 35. Multipliers over compact groups

Section 36. More on multipliers over compact groups

Section 37. Lacunar/ty for compact groups

Section 38. Ideal theory for certain convolution algebras on compact

         groups

Chapter Ten: Spectral synthesis

Section 39. Ideals in regular commutative Banach algebras

Section 40. Preliminaries on spectral sets

Section 41. Some special sets

Section 42. The failure of spectral synthesis in □(G)

Chapter Eleven: Miscellany

Section 43. transforms and maximal functions

Section 44. Pointwise summability for Fourier transforms

Appendix D: Tensor products and yon Neumann norms

Appendix E: Miscellaneous facts from functional analysis

Addendum to Volume I

Bibliography

Index of symbols

Index of authors and terms