Book contents
- Frontmatter
- Preface
- Contents
- INTRODUCTION
- ABOUT THIS BOOK
- CHAPTER I TRIGONOMETRIC SERIES AND SETS OF UNIQUENESS
- CHAPTER II THE ALGEBRA A OF FUNCTIONS WITH ABSOLUTELY CONVERGENT FOURIER SERIES, PSEUDOFUNCTIONS AND PSEUDOMEASURES
- CHAPTER III SYMMETRIC PERFECT SETS AND THE SALEM-ZYGMUND THEOREM
- CHAPTER IV CLASSIFICATION OF THE COMPLEXITY OF U
- CHAPTER V THE PIATETSKI-SHAPIRO HIERARCHY OF U-SETS
- CHAPTER VI DECOMPOSING U-SETS INTO SIMPLER SETS
- CHAPTER VII THE SHRINKING METHOD, THE THEOREM OF KÖRNER AND KAUFMAN, AND THE SOLUTION TO THE BOREL BASIS PROBLEM FOR U
- CHAPTER VIII EXTENDED UNIQUENESS SETS
- CHAPTER IX CHARACTERIZING RAJCHMAN MEASURES
- CHAPTER X SETS OF RESOLUTION AND SYNTHESIS
- LIST OF PROBLEMS
- REFERENCES
- SYMBOLS AND ABBREVIATIONS
- INDEX
Preface
Published online by Cambridge University Press: 07 September 2010
- Frontmatter
- Preface
- Contents
- INTRODUCTION
- ABOUT THIS BOOK
- CHAPTER I TRIGONOMETRIC SERIES AND SETS OF UNIQUENESS
- CHAPTER II THE ALGEBRA A OF FUNCTIONS WITH ABSOLUTELY CONVERGENT FOURIER SERIES, PSEUDOFUNCTIONS AND PSEUDOMEASURES
- CHAPTER III SYMMETRIC PERFECT SETS AND THE SALEM-ZYGMUND THEOREM
- CHAPTER IV CLASSIFICATION OF THE COMPLEXITY OF U
- CHAPTER V THE PIATETSKI-SHAPIRO HIERARCHY OF U-SETS
- CHAPTER VI DECOMPOSING U-SETS INTO SIMPLER SETS
- CHAPTER VII THE SHRINKING METHOD, THE THEOREM OF KÖRNER AND KAUFMAN, AND THE SOLUTION TO THE BOREL BASIS PROBLEM FOR U
- CHAPTER VIII EXTENDED UNIQUENESS SETS
- CHAPTER IX CHARACTERIZING RAJCHMAN MEASURES
- CHAPTER X SETS OF RESOLUTION AND SYNTHESIS
- LIST OF PROBLEMS
- REFERENCES
- SYMBOLS AND ABBREVIATIONS
- INDEX
Summary
This book grew out of a set of notes prepared during the course of a joint Caltech-UCLA Seminar in Descriptive Set Theory and Harmonic Analysis, organized by the authors during the academic year 1985–86. We appreciate very much the help as well as the patience of the participants in this seminar.
We are grateful to G. Debs, R. Dougherty, S. Jackson, R. Kaufman, R. Lyons, and J. Saint Raymond for many valuable comments and suggestions. The first author is indebted to S. Pichorides for introducing him to the subject of uniqueness for trigonometric series. We would like also to thank N. O'Connor for her efficiency, care and patience in typing the manuscript.
The work of A. S. Kechris has been partially supported by NSF Gratnt DMS84-16349. A. Louveau has been supported by CNRS, France and by UCLA during his visit in the academic year 1985–86. He takes this opportunity to thank the Mathematics Department for its hospitality.
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- Publisher: Cambridge University PressPrint publication year: 1987