Descriptive set theory and the structure of sets of uniqueness
 Responsibility
 Alexander S. Kechris and Alain Louveau.
 Imprint
 Cambridge [Cambridgeshire] ; New York : Cambridge University Press, 1987.
 Physical description
 1 online resource (367 pages) : illustrations
 Series
 London Mathematical Society lecture note series ; 128.
Online
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Description
Creators/Contributors
 Author/Creator
 Kechris, A. S., 1946
 Contributor
 Louveau, Alain.
Contents/Summary
 Bibliography
 Includes bibliographical references (pages 353358) and index.
 Contents

 Introduction
 About this book
 1. Trigonometric series and sets of uniqueness
 2. The algebra A of functions with absolutely convergent fourier series, pseudofunctions and pseudomeasures
 3. Symmetric perfect sets and the SalemZygmund theorem
 4. Classification of the complexity of U
 5. The PiatetskiShapiro hierarchy of Usets
 6. Decomposing Usets into simpler sets
 7. The shrinking method, the theorem of Koerner and Kaufman, and the solution to the Borel basis problem for U
 8. Extended uniqueness sets
 9. Characterizing Rajchman measures
 10. Sets of resolution and synthesis
 List of problems
 References
 Symbols and Abbreviations
 Index.
 (source: Nielsen Book Data)
 Publisher's summary

The study of sets of uniqueness for trigonometric series has a long history, originating in the work of Riemann, Heine, and Cantor in the midnineteenth century. Since then it has been a fertile ground for numerous investigations involving real analysis, classical and abstract harmonic analysis, measure theory, functional analysis and number theory. In this book are developed the intriguing and surprising connections that the subject has with descriptive set theory. These have only been discovered recently and the authors present here this novel theory which leads to many new results concerning the structure of sets of uniqueness and include solutions to some of the classical problems in this area. In order to make the material accessible to logicians, set theorists and analysts, the authors have covered in some detail large parts of the classical and modern theory of sets of uniqueness as well as the relevant parts of descriptive set theory. Thus the book is essentially selfcontained and will make an excellent introduction to the subject for graduate students and research workers in set theory and analysis.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 1987
 Series
 London Mathematical Society lecture note series ; 128
 Related Work
 Sets of uniqueness.
 ISBN
 9781107361492 (electronic bk.)
 1107361494 (electronic bk.)
 0521358116
 9780521358118
 9780511758850